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(Soft music plays)
A title screen over a blue sky reads, Today’s Junior Lesson: Predicting Through Probability.
A female announcer says,
WELCOME TO
TVOKIDS POWER HOUR
OF LEARNING.
A brown haired woman wearing glasses and a leopard print shirt, sits at a table in her home.
A black and white photograph of downtown Toronto hangs on the wall behind her.
The woman says, HELLO, STUDENTS. HOW ARE YOU?
WELCOME TO ANOTHER EPISODE OF
TVOKIDS POWER HOUR OF LEARNING.
A caption appears that reads, Junior 4-6. Teacher Vanessa.
The woman continues, MY NAME IS TEACHER VANESSA,
AND I'M SO EXCITED TO SPEND
THE NEXT 60 MINUTES TOGETHER
LEARNING, HAVING A LOT OF FUN,
AND SHARING A FEW LAUGHS
TOGETHER.
BUT BEFORE WE BEGIN,
I'M HOPING THAT
YOU'VE BEEN PRACTISING
OUR POSITIVE AFFIRMATIONS THAT
WE LEARNED A FEW WEEKS AGO.
THESE ARE POSITIVE STATEMENTS
CALLED MANTRAS,
AND THEY HELP US BUILD
OUR SELF-CONFIDENCE
BY REPEATING THEM
OVER AND OVER EACH DAY.
SO, I'M GOING TO TELL YOU
OUR THREE MANTRAS,
AND I WOULD LOVE FOR YOU
TO REPEAT AFTER ME.
ARE YOU READY?
I AM CAPABLE.
LET ME HEAR YOU.
Vanessa holds her hand to her ear.
I AM A MATH PERSON.
GOOD JOB. AND I CAN DO IT.
AWESOME. I CAN HEAR YOU
ALL THE WAY FROM STONEY CREEK.
SO, TODAY WE'RE GOING TO BE
TALKING ABOUT PROBABILITY.
WHAT ARE THE ODDS
OF SOMETHING HAPPENING?
AND BEFORE WE BEGIN,
I WAS THINKING THAT
I COULD BRING MY SON CHASE OUT
TO PLAY A PROBABILITY GAME
AND GET US WARMED UP
FOR SOME GREAT LEARNING
OVER THE NEXT HOUR.
A young brown-haired boy, Chase, hops behind Vanessa. He wears a black T-shirt
Vanessa says, WELCOME, CHASE.
COME ON IN.
SO, WHAT WE'RE GOING TO
BE DOING--
JUST STAND BESIDE ME,
RIGHT HERE.
RIGHT HERE,
ON THE TABLE.
ARE YOU READY TO PLAY
A MATH GAME?
A caption reads, Junior 4-6. Chase.
Chase says, YEAH!
Vanessa says, OKAY. SO, STAND UP
NICE AND STRAIGHT
SO EVERYBODY
CAN SEE YOU.
OKAY. SO, I AM GOING TO
ROLL A DICE,
AND WHATEVER NUMBER
WE LAND ON,
THAT'S HOW MANY
EXERCISES--
YEAH. ARE YOU READY
TO SHOW THE KIDS
SOME EXERCISES?
SO, BEFORE YOU BEGIN,
MAKE SURE THAT YOU HAVE
A BIG SPACE
TO DO SOME EXERCISES,
JUST LIKE CHASE IS.
MAKE SURE
YOU CAN SPREAD OUT
AND HAVE A LOT
OF ROOM.
SO, WE'RE GOING TO
GET OUR BODIES READY
SO THAT OUR MINDS
WILL BE READY TO LEARN.
I'M GOING TO ROLL
THE FIRST DICE,
AND IT LANDS ON
A FOUR.
Vanessa holds up a large die made of brown cardboard paper.
Vanessa says, SO, CHASE, DO YOU MIND
DOING FOUR JUMPING JACKS?
Chase does jumping jacks and counts, OKAY. ONE, TWO, THREE, FOUR.
Vanessa says, AWESOME. NEXT ROLL.
Vanessa rolls the die and says, A ONE. HOW ABOUT YOU DO
ONE NECK CIRCLE?
Chase and Vanessa do a neck circle.
Vanessa says, NEXT ROLL, WE HAVE
A ONE AGAIN.
HOW ABOUT ONE HIGH KNEE?
Chase raises his left knee.
Vanessa says, OKAY. LAST ROLL.
ARE YOU READY?
Chase says, YEAH.
Vanessa rolls the die and says, SIX. LET'S DO
SIX ARM CIRCLES
TO GET OUR ARMS READY TO
WRITE AND PLAY SOME GAMES.
Chase circles his arms and counts, ONE, TWO, THREE, FOUR,
FIVE, SIX.
Vanessa says, ALL RIGHT. AND LET'S TAKE
SOME BIG, DEEP BREATHS
BEFORE WE BEGIN,
CHASE.
(BOTH INHALING AND EXHALING)
Vanessa says, ONE MORE.
(INHALING AND EXHALING)
Vanessa continues, BREATHE OUT. AND SAY, "BYE
AND THANK YOU" TO EVERYBODY.
Chase waves and says, BYE.
Vanessa says, THANK YOU
FOR JOINING US, CHASE.
An animated sun rises.
Notes on a tabletop display beside Vanessa read, Probability, the likelihood of something happening.
Shown through a fraction and number line. Use probability to make decisions and predictions.
Vanessa says, SO, TODAY, WE'RE GOING TO
TALK ABOUT PROBABILITY,
THE LIKELIHOOD
OF AN EVENT OCCURRING.
HAVE YOU EVER WONDERED
WHAT THE WEATHER PERSON
IS TALKING ABOUT WHEN THEY SAY,
"THERE'S A 50% CHANCE
OF RAIN OR SNOW"?
OR IF YOU HAVE A VERY SMALL
CHANCE OF WINNING THE LOTTERY?
WHAT ARE THEY TALKING ABOUT?
TODAY, I'M GOING TO SHOW YOU
HOW YOU CAN SOLVE
FOR PROBABILITY
USING FRACTIONS
AND A NUMBER LINE.
WE'RE GOING TO USE PROBABILITY
TO MAKE DECISIONS
AND FUTURE PREDICTIONS.
SO, IF YOU HEARD THAT
THERE WAS A SNOWSTORM COMING,
YOU WOULD PRETTY--
YOU'D BE PRETTY WELL
TO BRING SNOW PANTS
AND MITTENS TO SCHOOL THAT DAY,
SO YOU'RE PREPARED FOR
THE WEATHER.
WE'RE GOING TO PLAY SOME
FUN GAMES TODAY WITH SPINNERS,
DICE AND CARDS.
SO, I WOULD LOVE FOR YOU
TO GET THOSE MATERIALS
IF YOU HAVE THEM LAYING AROUND,
OR YOU COULD MAKE
YOUR OWN CARDS.
YOU COULD MAKE YOUR OWN DICE.
I MADE THESE OUT OF
A PIECE OF CARDBOARD.
IT'S VERY SIMPLE. ALL YOU NEED
TO MAKE THE CARDBOARD DIE
ARE TAPE, CARDBOARD AND MARKERS.
IF YOU HAVE SOMETHING LIKE
A LAZY SUSAN LAYING AROUND--
YOUR PARENTS
WILL KNOW WHAT THAT IS--
YOU CAN TAPE SOME PAPER TO IT
AND IT'LL SPIN LIKE A SPINNER,
OKAY?
Vanessa holds up a lazy susan covered with colored paper in white, blue, red and yellow quadrants.
Vanessa says, I USED JUST YOUR RUN-OF-THE-MILL
DECK OF CARDS.
IF YOU HAVE A COIN OR TWO,
WE COULD DO SOME COIN TOSSES
LATER ON.
I'M GOING TO SHOW YOU SOME
REALLY COOL GAMES AND ACTIVITIES
YOU COULD DO WITH YOUR FRIENDS.
BUT BEFORE WE DO, LET'S WATCH
THIS EPISODE OF
LADY VOCAB,
WHO'S GOING TO GO INTO
THE DEFINITION OF PROBABILITY
USING A REALLY COOL SONG.
CHECK IT OUT, AND I'LL CATCH YOU
BACK HERE AFTER.
The animated sun rises.
A title screen reads, The Lady Vocab Show.
Professor P stands in a dark room in front of a monitor ‘with Lady Vocab’ written several times on it.
He wears a black sweater with a large letter P on the front. He has short dark hair and wears glasses.
Professor P says, HEY THERE, WORD FANS,
AND WELCOME TO
THE
LADY VOCAB SHOW.
I'M YOUR HOST,
PROFESSOR P.
AND NOW TO INTRODUCE
THE LONG-WINDED LADY HERSELF,
LADY VOCAB.
Lady Vocab stands behind a microphone.
She has shoulder length blonde hair and wears large sparkling silver glasses, and a black and white costume with the words window, shuttle, machine, and package written on it.
She says, THANKS, PROFESSOR.
ARE YOU READY
TO ROCK THE WORD?
Professor P says, YES, INDEEDY, MILADY.
THE WORD IS "PROBABILITY,"
WHICH IS A TERM THAT MEANS
HOW LIKELY SOMETHING
IS TO HAPPEN.
Lady Vocab says, HIT IT.
(Electronic music plays)
She sings, P-R-O-B-A-B-I-L-I-T-Y
Professor P says, PROBABILITY.
Lady Vocab sings, THE CHANCES THAT
YOU'RE LIKELY TO SUCCEED
JUST USE PROBABILITY
Professor P says, MM-HMM.
Lady Vocab sings, TOSS A COIN, IT'S 50-50
Professor P says, COULD BE HEADS
OR TAILS.
Lady Vocab sings, THE OUTCOME
IS FOR YOU TO SEE
Professor P says, THAT'S RIGHT.
Lady Vocab sings, PROBABILITY
SEEMS LIKELY
Professor P says, MM-HMM.
COULD BE.
Lady Vocab sings, PROBABILITY
CHANCES MAKE YOU LUCKY
Professor P says, HOW LIKELY?
Lady Vocab sings, PROBABILITY.
Professor P says, HMM. WELL, THERE YOU HAVE IT.
THE LIKELIHOOD THAT
I'LL SEE YOU NEXT TIME?
100%, WORD FANS. BYE FOR NOW.
Lady Vocab sings, PROBABILITY
YOU'RE SO LUCKY, PROBABILITY
A red logo over a black background reads, TVO kids. Copyright, The Ontario Educational Commissions Authority MMXIV
The animated sun rises.
Vanessa says, WELCOME BACK.
SO, TODAY WE'RE GOING TO TALK
ABOUT THEORETICAL PROBABILITY.
The caption reads, Junior 4-6. Teacher Vanessa.
A formula written on the tabletop display reads, theoretical probability equals number of favorable outcomes divided by number of possible outcomes.
Vanessa continues, WHAT DOES THAT MEAN?
WHAT ARE YOUR ODDS OF WINNING
WHEN YOU PLAY A GAME?
WHAT ARE YOUR ODDS
OF ROLLING ANY NUMBER ON A DICE?
Vanessa holds up a die.
She continues, WHAT ARE THE ODDS OF GETTING
A HEADS OR TAILS
WHEN YOU FLIP A COIN?
Vanessa holds up a coin.
She continues, AND IF YOU WANTED TO PLAY A GAME
WITH YOUR FRIENDS,
WHAT ARE THE ODDS OF PICKING UP
AN EIGHT IN CRAZY EIGHTS?
LET'S FIGURE THIS OUT.
SO, THEORETICAL PROBABILITY,
OR PROBABILITY,
IS KNOWN AS THE NUMBER
OF FAVOURABLE OUTCOMES
OVER, OR DIVIDED BY
IN A FRACTION FORM,
THE NUMBER OF POSSIBLE OUTCOMES.
SO, WHAT DOES THAT MEAN?
LET'S SAY I HAVE A DICE.
WE KNOW THAT THERE ARE SIX SIDES
TO A DICE,
AND EVERY SIDE HAS A NUMBER
RANGING FROM ONE TO SIX.
Vanessa rolls the die and says, SO, IF I WERE TO ROLL THIS DICE
AND I GET THE NUMBER SIX,
TECHNICALLY I HAVE
A ONE-OUT-OF-SIX PROBABILITY
OF GETTING ANY NUMBER
ON THIS DICE.
IN THIS CASE, I DID ROLL A SIX.
OKAY?
SO, LET'S SAY
I SAID TO MY FRIEND,
"IF I ROLL A FIVE,
I WIN THE GAME."
WHAT ARE MY ODDS OF WINNING?
I KNOW THAT I HAVE TO ROLL
JUST A FIVE,
SO THAT WOULD JUST BE A ONE,
LIKE WE HAVE HERE.
Vanessa holds up a blue card with the fraction 1/6 written on it.
She says, AND THERE ARE
SIX POSSIBLE OUTCOMES
'CAUSE THERE ARE SIX NUMBERS
ON A DICE.
SO, I HAVE A ONE-IN-SIX ODD
OF WINNING THE GAME.
LET'S SEE IF I DID WIN.
Vanessa rolls the die.
She says, NO. I ROLLED A FOUR.
SO UNFORTUNATELY,
MY FRIEND WON THAT ROUND.
FORTUNATELY FOR HER.
OKAY?
Vanessa removes the formula from the display, then picks up the lazy Susan spinner.
She says, LET'S TRY PLAYING WITH
OUR SPINNER.
AND WE HAVE
ONE, TWO, THREE, FOUR
DIFFERENT-COLOURED SECTIONS.
THAT MEANS THE SPINNER
CAN LAND ON
ANY ONE OF THE FOUR SECTIONS.
SO, MY POSSIBILITY--
PROBABILITY OF LANDING
ON THE WHITE, FOR EXAMPLE,
IS ONE OVER FOUR.
MY PROBABILITY OF LANDING
ON THE BLUE
IS ONE OUT OF THE TOTAL OF FOUR
DIFFERENT OPTIONS THERE ARE.
SO, YOU MIGHT SAY
TO YOUR FRIEND,
"IF I LAND ON RED, I WIN,
"BUT IF YOU LAND--
WHEN YOU SPIN AND YOU LAND
ON BLUE, YOU WIN."
SO, LET'S JUST SAY-- LET'S TRY.
I'M GOING TO SAY IF I LAND
ON RED, I GET ONE POINT.
Vanessa spins the spinner and says,
SO, I HAVE MY SPINNER.
I'M GOING TO TURN IT AROUND
AND UNFORTUNATELY,
I LANDED ON--
OH, WAIT, (UNCLEAR).
OH, NO. I LANDED ON THE WHITE.
SO, I DIDN'T GET A POINT, OKAY?
SO, LET'S SAY
IT'S MY FRIEND'S TURN.
AND THIS IS HARDER THAN IT SEEMS
TO HOLD.
(LAUGHING)
Vanessa spins the spinner and says,
AND IT LANDS ON BLUE,
BUT SHE NEEDED RED TO WIN.
SHE DOESN'T WIN.
SO, EITHER WAY, ONE OF US--
OR EACH OF US, I SHOULD SAY,
HAS A ONE-IN-FOUR CHANCE
OF WINNING THAT GAME.
IF I SAID I NEED TO LAND
ON RED
OR
BLUE TO WIN,
WHAT IS MY POSSIBILITY NOW,
MY PROBABILITY OF WINNING?
WE HAVE ONE-HALF.
WHY IS THAT ONE-HALF?
BECAUSE I COULD WIN ONE, TWO
OF A POSSIBLE
ONE, TWO, THREE, FOUR.
SO, TWO OUT OF FOUR
IS THE SAME AS
HAVING THE ODDS
OF HAVING ONE-HALF.
Vanessa holds up a blue card with the fraction 1/2 on it.
She says, SO, PLOTTING THIS
ON A NUMBER LINE,
I'M GOING TO SHOW YOU
SOME TERMS...
Vanessa picks up a long brown sheet of paper with a number line drawn on it.
Notes on the line from left to right read, impossible, unlikely, equally likely, likely, and certain.
The number 0 is at the left end. The number 1 is at the right.
Vanessa continues, ...THAT YOU ARE GOING TO BE
USING
IN MATHEMATICS FOR PROBABILITY.
I LOVE THE NUMBER LINE.
SO, IN THIS CASE
FOR PROBABILITY,
WE HAVE "UNLIKELY"
AND "IMPOSSIBLE"
STARTING AT THE ZERO.
SO, FOR EXAMPLE, YOUR ODDS
OF WINNING THE LOTTERY
ARE VERY, VERY UNLIKELY.
NOT IMPOSSIBLE,
'CAUSE "IMPOSSIBLE" MEANS
IT COULD NEVER HAPPEN.
BUT SOMEWHERE IN THE REALM OF
UNLIKELY TO IMPOSSIBLE.
SO, "IMPOSSIBLE" COULD BE
"THE SUN WON'T RISE TOMORROW,"
WHEN WE KNOW THAT CERTAINLY,
THE SUN WILL RISE EVERY DAY.
SO, WE'RE GOING TO MOVE
FROM IMPOSSIBLE TO UNLIKELY.
LIKE WE SAID,
WINNING THE LOTTERY,
LIKE WE SAID, SPINNING, UM,
MAYBE A WHEEL THAT HAD
A HUNDRED NUMBERS ON IT
AND YOU HAVE TO GET
ONE OF THE NUMBERS.
IT'S VERY UNLIKELY THAT
THE WHEEL WILL SPIN
ON YOUR NUMBER,
FROM ONE OUT OF A HUNDRED.
OKAY? AGAIN, NOT IMPOSSIBLE,
'CAUSE IT MIGHT HAPPEN.
BUT IT COULD BE UNLIKELY.
"EQUALLY LIKELY" MEANS
SOMETHING WILL HAPPEN
AS LIKELY AS IT WILL NOT HAPPEN.
SO, IF I PICK UP A COIN,
FOR EXAMPLE,
I KNOW THAT IT HAS A HEAD
AND A TAIL.
AND BECAUSE THERE'S
ONLY TWO OPTIONS, AGAIN,
I HAVE A ONE-OUT-OF-TWO ODD
OR PROBABILITY
THAT I WOULD ROLL-- OR, SORRY.
FLIP A COIN
AND LAND ON A HEAD.
I HAVE A ONE-IN-TWO PROBABILITY,
THEN,
THAT IT WOULD ALSO--
IT WOULD LAND ON A TAIL.
OKAY? SO, WHEN SOMETHING
IS EQUALLY LIKELY TO HAPPEN
AS IT'S
NOT LIKELY TO HAPPEN,
YOU HAVE A 50-50 CHANCE,
A ONE-OUT-OF-TWO SHOT,
IT IS EQUALLY LIKELY.
A yellow star is in the middle of the number line over the number 0.5.
Vanessa says, UM, SO, FOR SOMETHING TO BE
LIKELY TO HAPPEN,
WE CAN TALK ABOUT SOMETHING LIKE
IF THE WEATHER PERSON SAYS
THERE'S A 75% CHANCE
OF RAIN TODAY,
THAT IS LIKELY
THAT IT WILL HAPPEN.
HOW DO WE KNOW? WE KNEW THAT
SOMETHING CLOSER TO ONE
IS ABSOLUTELY CERTAIN TO HAPPEN.
SO, FOR EXAMPLE,
IF WE SAID YOU HAVE, UM--
IF YOU SPUN A WHEEL
AND IF YOU GOT ANY OF
THE THREE COLOURS EXCEPT WHITE,
YOU WIN, THAT IS LIKELY
THAT YOU WILL WIN THAT GAME,
BECAUSE YOU COULD LAND
ON YELLOW, RED, BLUE,
AND STILL WIN.
THE ONLY WAY YOU WOULD LOSE IS
IF YOU LANDED ON WHITE.
SO, THAT IS
A LIKELY PROBABILITY
THAT YOU WILL WIN.
SOMETHING CERTAIN IS THAT
YOU WILL TURN PLUS-ONE
ON YOUR NEXT BIRTHDAY.
SO, IF YOU ARE NINE, ON YOUR
NEXT BIRTHDAY YOU WILL TURN 10.
IF YOU'RE 10,
ON YOUR NEXT BIRTHDAY
YOU WILL CERTAINLY TURN 11.
YOU ARE AN AWESOME PERSON.
THAT IS CERTAIN.
SO, THAT'S 100% POSSIBILITY.
YOU'RE GREAT AT MATH?
100% POSSIBILITY. TRUST ME.
OKAY? SO, WE HAVE THE RANGE OF
SOMETHING IMPOSSIBLE HAPPENING,
OKAY?
SO AGAIN, WE SAID THAT
UNFORTUNATELY,
IF YOU THOUGHT THAT
THE SUN WILL NOT RISE TOMORROW,
IMPOSSIBLE.
YOU MIGHT WIN THE LOTTERY?
SOMEWHERE IN THE REALM
OF UNLIKELY AND IMPOSSIBLE.
SO, EVERY DAY, WHEN YOU BUY
YOUR LOTTERY TICKET,
AND YOU HAVE A 1 IN 33,000,000
CHANCE OF WINNING,
UNFORTUNATELY THE ODDS ARE
VERY, VERY LOW THAT YOU WIN,
BUT THEY'RE NOT IMPOSSIBLE.
SO, WE HAVE
"WINNING THE LOTTERY"
WOULD BE SOMEWHERE POSSIBLY
CLOSER TO THE ZERO HERE.
BUT DON'T GIVE UP HOPE, FRIENDS,
AS YOU GET OLDER.
(LAUGHING)
AGAIN, "EQUALLY LIKELY,"
WE'RE TALKING ABOUT
FLIPPING A COIN
AND THERE'S ONLY TWO OPTIONS.
(CLEARING THROAT)
WE'RE
TALKING ABOUT PLAYING CARDS,
WHEN YOU ONLY HAVE
RED OR BLACK SUITS.
Vanessa holds up two playing cards.
She continues, YOU'RE EQUALLY LIKELY
TO PICK UP A RED CARD
AS YOU ARE A BLACK CARD.
WE HAVE SOMETHING "LIKELY"
AS 75%,
OR THREE OVER FOUR.
WE TALKED ABOUT THE SPINNER.
WE SAID YOU WON--
WHEN THE GAME IS YOU CHOOSE
RED, YELLOW OR BLUE
OUT OF A TOTAL OF FOUR OPTIONS,
IT'S LIKELY THAT YOU WILL WIN.
AND THEN "CERTAIN," WE TALKED
ABOUT YOU GETTING A YEAR OLDER
FOR YOUR AGE NEXT YEAR, AND FOR
THE SUN SETTING THE NEXT DAY.
SO, WHEN YOU'RE WATCHING TV
AND MAYBE YOU'RE CATCHING
YOUR PARENTS WATCHING THE NEWS,
AND THE WEATHER PERSON SAYS,
"THERE'S A 10% CHANCE
OF PRECIPITATION TONIGHT,"
Vanessa holds a sheet of paper that reads, unlikely, 10%, 1/10, 0.1.
She continues, OKAY, THAT MEANS THAT
THERE'S A ONE-IN-10 CHANCE
OF IT RAINING TONIGHT.
THIS IS EQUIVALENT, MEANING
THAT IT'S THE SAME THING,
WHICH ALSO IS EQUIVALENT TO
ONE-TENTH OUT OF ONE,
FROM ZERO TO ONE.
SO, AGAIN, VERY, VERY UNLIKELY
THAT THIS WOULD HAPPEN.
OKAY? VERY UNLIKELY
FOR THERE TO BE RAIN TODAY.
Vanessa holds a sheet of paper that reads, equally likely, 50%, 5/10, 0.5.
She says, SIMILARLY,
IF SHE SAYS THERE'S A 50--
HE OR SHE SAYS THERE'S
A 50% CHANCE OF RAIN TODAY,
WE KNOW THAT
THAT'S EQUALLY LIKELY.
IT MIGHT RAIN
AS MUCH AS IT MIGHT NOT RAIN.
OKAY? SO, IN THIS CASE,
BETTER TO BE SAFE THAN SORRY.
I WOULD BRING AN UMBRELLA
OR A RAIN JACKET,
WHEREVER YOU'RE GOING.
Vanessa holds a sheet of paper that reads, certain, 90%, 9/10, 0.9.
Vanessa continues, AND IF SHE SAID--
OR HE SAID, I SHOULD SAY--
A 90% CHANCE OF RAIN TODAY,
IT'S ALMOST CERTAIN
THAT IT'S GOING TO RAIN.
SO, IN THIS CASE,
I WOULD USE THIS PROBABILITY
TO MAKE A DECISION
AND BRING AN UMBRELLA,
RAIN JACKET, RAIN BOOTS
TO SCHOOL
OR WHEREVER YOU'RE GOING TO PLAY
THAT DAY.
SO, YOU SEE
Vanessa holds up the number line and continues,
FROM OUR NUMBER LINE
THAT PROBABILITY RANGES
FROM ZERO, WHICH MEANS,
WHICH IS-- SORRY--
EXTREMELY UNLIKELY, IMPOSSIBLE.
TO ONE, WHICH IS MEANING
CERTAINLY SOMETHING WILL HAPPEN.
OKAY?
SO, IN THE NEXT SEGMENT,
WHEN WE TALK ABOUT
DIFFERENT GAMES,
WE'RE GOING TO PLOT THIS
AND DIFFERENT SCENARIOS
THAT YOU MIGHT DEAL WITH
ON A DAILY BASIS
ON OUR NUMBER LINE.
LET'S PLAY ONE MORE GAME
BEFORE WE WATCH OUR NEXT SHOW.
I HAVE A DECK OF CARDS HERE.
AND THEY RANGE FROM ACE
ALL THE WAY UP TO 10, AND
THEN WE HAVE THREE FACE CARDS
WITH THE ACE.
SORRY. THREE FACE CARDS.
SO, EACH SUIT HAS 13 CARDS.
WE HAVE THE HEARTS,
THE DIAMONDS, THE SPADES
AND THE CLUBS.
Vanessa shuffles a deck of cards and says,
IF I SAID TO YOU, "WHAT ARE
THE ODDS OF PICKING UP
A SUIT OF HEARTS
OUT OF MY DECK,"
WHAT WOULD THE ODDS BE?
Vanessa puts the formula back onto the display and says,
KNOWING THAT OUR
THEORETICAL PROBABILITY, AGAIN,
IS THE NUMBER
OF FAVOURABLE OUTCOMES--
SO, WE KNOW THAT THERE ARE
13 HEARTS IN OUR DECK.
OVER HOW MANY TOTAL
OR POSSIBLE OUTCOMES ARE THERE.
WE KNOW THAT THERE ARE 52 CARDS
IN THE DECK.
SO, 13 OVER 52
IS OUR FRACTION THAT WE USE,
Vanessa holds up a blue card with the fraction 13/52 on it.
She continues, WHICH IS THE SAME THING
AS ONE OVER FOUR.
SO, WE HAVE
A ONE-OUT-OF-FOUR CHANCE
OF PICKING UP A HEART WHEN I...
...QUICKLY SHUFFLE.
AND I'M GOING TO PICK
THE FIRST CARD ON TOP.
SO, I HAVE
A ONE-OUT-OF-FOUR CHANCE,
WHICH UNFORTUNATELY IS UNLIKELY.
OR MAYBE YOU DON'T WANT
TO PICK A HEART.
THAT'S YOUR FAVOURITE SUIT.
BUT LET'S SAY IT'S UNLIKELY
THAT YOU'RE GOING TO PICK
A HEART, A CARD THAT HAS
THE SUIT OF A HEART IN IT.
COMPARED TO--
THERE'S STILL CLUBS.
THERE'S STILL SPADES.
AND THERE'S STILL DIAMONDS.
SO, YOU'RE MORE LIKELY TO PICK
ONE OF THE OTHER THREE SUITS
THAT ARE REMAINING.
SO, ARE YOU READY TO SEE
IF I CAN PICK A HEART?
Vanessa draws the ace of hearts out of the deck of cards.
She says, OH, MY GOODNESS!
I DID.
(LAUGHING)
OKAY. SO, EVEN THOUGH MY ODDS
WERE UNLIKELY
THAT I WOULD PICK THIS,
ONE OUT OF FOUR,
I WAS STILL ABLE TO DO IT.
SO, THERE'S STILL HOPE OUT THERE
FOR ALL OUR LOTTERY PLAYERS.
ANYWAYS, I WOULD LIKE NOW
JUST TO THROW TO HAMZA,
AND HE IS FROM THE SHOW
LOOK KOOL,
AND HE'S GOING TO GO THROUGH
SOME AWESOME PROBABILITY GAMES,
EXPERIMENTS AND DEFINITIONS
OVER THE COURSE OF
A FEW MINUTES.
I HOPE YOU REALLY ENJOY,
AND I'LL SEE
ALL YOU PROBABILITY LOVERS
HERE AFTER THE VIDEO.
The animated sun rises.
Hamza flips a coin. He is clean shaven with short dark hair.
He wears a navy blue dress shirt and an orange and white striped bow tie.
Hamza says, OKAY.
HEADS.
TAILS? LET'S TRY IT AGAIN.
TAILS.
HEADS?
WHAT ARE THE ODDS I'M EVER
GOING TO GET THIS RIGHT?
TO FIND OUT,
WE'LL MEET A BIG CARD...
A man wearing Jack of Hearts costume enters the room.
(IN FRENCH ACCENT)
The man says, I AM JACQUES DESCARTES.
Hamza says, YEAH. YOU'RE THE ONE I NEEDED
TO WIN GO FISH YESTERDAY.
A clip plays.
...LAUNCH POWERFUL ROCKETS
YOU CAN BUILD AT HOME...
WHOA!
...AND DISCOVER AN UNBELIEVABLE
SCIENTIFIC FACT...
A young girl kneels and puts a microphone to a small white dog’s face.
She says, WHEN'S YOUR BIRTHDAY?
MINE IS NOVEMBER 9TH.
OH. WE HAVE A MATCH.
Hamza says, ...ON
LOOK KOOL.
(Upbeat music plays)
Hamza spins and puts on sunglasses. He wears a blue shirt and a white and blue striped bow tie.
Colorful geometric shapes fall onto a grassy field. The shapes grow to form a colorful city skyline.
(KOOL KATT MEOWING)
Colorful bridges form over a river. A yellow staircase rotates around a red tower.
A purple airplane circles the tower. Koolkatt watches an orange tower rise from the ground.
The title, Look Kool appears over a blue sky.
A coin shoots out of KoolKatt’s toaster-shaped back.
Hamza catches it and says, HEADS.
TAILS AGAIN.
HOW IS THIS POSSIBLE?
THAT'S, LIKE, 10 IN A ROW NOW.
KOOL CAT AND I
ARE PLAYING FLIP THE COIN.
AND SO FAR, HE'S WON EVERY TIME.
(LAUGHING)
MAYBE I NEED SOME OLD FASHIONED
LUCKY CHARMS,
LIKE THIS FOUR-LEAF CLOVER
AND THIS HORSESHOE.
OKAY, OKAY. ONE MORE.
ONE MORE. LET'S GO.
KoolKatt shoots out another coin.
Hamza catches it and says, HEADS.
TAILS AGAIN.
HOW IS THIS POSSIBLE?
THAT'S, LIKE, 10 IN A ROW NOW.
IT LOOKS LIKE
YOU COULD USE SOME HELP.
WHO ARE YOU?
Jacques enters the room.
He says, I AM JACQUES DESCARTES.
PERHAPS YOU REMEMBER ME
FROM YOUR DECK OF CARDS, NO?
Hamza says, YEAH. YOU'RE THE ONE I NEEDED
TO WIN GO FISH YESTERDAY.
NOW YOU DECIDE TO SHOW UP?
Jacques says, AND DO NOT BLAME ME
FOR PROBABILITY.
I DO NOT MAKE THE RULES.
Hamza says, PROBABILITY? WHAT'S THAT?
Jacques says, PROBABILITY IS A TYPE OF MATH
THAT HELPS PREDICT HOW LIKELY
SOMETHING IS TO HAPPEN.
Hamza says, WAIT. YOU MEAN MATH
CAN TELL ME HOW LIKELY IT IS
I'LL GET THE CARD I NEED
IN GO FISH,
OR WIN A COIN TOSS?
Jacques says, UH, YES.
I MEAN, WE CARDS KNOW ABOUT IT,
BUT WE PLAY
GAMES OF CHANCE ALL DAY LONG.
Hamza says, CAN YOU TELL ME
WHY KOOL CAT KEEPS WINNING?
Jacques says, I KNOW EXACTLY WHY KOOL CAT
KEEPS WINNING.
AND MAYBE YOU'LL FIGURE
THAT OUT FOR YOURSELF, EH?
(SNORTING ARROGANTLY)
KoolKatt shakes his head.
Hamza says, OKAY. CAN YOU TELL ME
HOW PROBABILITY WORKS?
Jacques says, OF COURSE.
PROBABILITY IS
THE NUMBER OF OUTCOMES YOU WANT
DIVIDED BY THE NUMBER
OF POSSIBLE OUTCOMES.
Hamza says, OH, OKAY.
SO, I WANT HEADS, AND THERE'S
ONLY TWO POSSIBLE OUTCOMES,
HEADS OR TAILS.
SO, THAT'S ONE DIVIDED BY TWO,
WHICH IS THE SAME AS ONE-HALF.
SO, TECHNICALLY, IT SHOULD BE
ON HEADS HALF THE TIME, RIGHT?
Jacques says, YOU'RE RIGHT.
IT SHOULD.
BUT EVEN WITH MY LUCKY
FOUR-LEAF CLOVER AND HORSESHOE,
KOOL CAT KEEPS WINNING.
Jacques snorts and says, LUCK HAS NOTHING TO DO WITH IT.
An animated 4-leaf clover walks through a field of clovers and says, OH, BOY. I FEEL LUCKY TODAY.
A brown shoe steps on the clover. The clover sticks to the bottom of the shoe, then frees itself.
The clover says, OOH. I SHOULD HAVE BROUGHT
MY LUCKY HORSESHOE.
A horseshoe falls on the clover.
The clover says, OH, MAN.
Hamza says, CAN YOU USE PROBABILITY
TO PREDICT
ANYTHING
OTHER THAN GAMES?
Jacques says, UH, YES, ABSOLUTELY.
I MEAN, PROBABILITY CAN TELL YOU
HOW LIKELY IT IS
THAT YOU'LL FIND A PEARL
IN AN OYSTER.
An animated oyster opens. A pearl is inside it.
Jacques continues, ONE IN 12,000.
OR HOW LIKELY IT IS THAT
A FAMILY WILL HAVE TRIPLETS.
ONE IN 44,000.
A picture of triplets appears.
Jacques continues, OR IT CAN TELL YOU
HOW LIKELY IT IS
THAT A GROWN-UP PERSON
WILL GO TO THE EMERGENCY ROOM
WITH A POGO STICK INJURY.
ONE IN 115,300.
A man hops on a pogo stick, then crashes.
The man says, OW!
Hamza says, SO, PROBABILITY IS AN
EXACT WAY TO LOOK AT THINGS?
Jacques says, UH, IT'S NOT EXACT.
BUT IT DOES SHOW YOU
HOW LIKELY OR UNLIKELY
IT IS TO HAPPEN.
Hamza says, OH, YEAH.
I MEAN, IF SOMETHING'S UNLIKELY,
THAT DOESN'T MEAN
THAT IT'S IMPOSSIBLE.
I MEAN, UNLIKELY THINGS
HAPPEN ALL THE TIME.
(Upbeat woodwind and tuba music plays)
Hamza flies through the sky wearing a pig costume. He flies in formation with several animated pigs.
He sings, NOT UNTIL PIGS FLY
THAT'S WHAT THEY SAY
WHEN SOMETHING'S UNLIKELY
BUT I'M HERE TODAY
FLAPPING MY WINGS
ON THE WAY TO THE SUN
THE ODDS WERE
200 TRILLION BILLION TO ONE
BUT JUST 'CAUSE IT'S RARE
DOESN'T MEAN IT'S NOT DONE
I SAID JUST 'CAUSE IT'S RARE
DOESN'T MEAN IT'S NOT DONE
OINK-OINK-OINK, OINK-OINK-OINK
OINK-OINK-OINK
SOMETIMES A RIVER
IS BACKWARDS FLOWING
SOMETIMES
A TURTLE IS NOT SO SLOWING
SOMETIMES IN SUMMER
IT STARTS SNOWING
AND NOW THAT
YOU'RE ALL KNOWING
I REALLY MUST BE GOING
OINK-OINK-OINK, OINK-OINK-OINK
OINK-OINK-OINK
Hamza says, SO, DO YOU THINK
KOOL KATT WINNING
10 TIMES IN A ROW
IS JUST PURE LUCK?
Jacques says, HA! I THINK
THAT'S AWFULLY IMPROBABLE.
Hamza says, YEAH. ME, TOO.
SO, WHAT ELSE CAN YOU TELL ME
ABOUT PROBABILITY?
Jacques says, OH, HERE IS ONE OF
MY FAVOURITE THINGS.
A graphic appears showing 23 human figures.
Jacques continues, IF YOU HAVE A ROOM OF 23 PEOPLE,
THERE IS A ONE IN TWO CHANCE
THAT TWO OF THEM
WILL HAVE THE SAME BIRTHDAY.
A box appears around two figures.
Hamza says, NOW, THAT DOESN'T
SOUND RIGHT.
I MEAN, THERE'S 23 PEOPLE
AND 365 DAYS IN A YEAR.
Jacques says, I DEAL IN PROBABILITY.
I KNOW WHAT I AM TALKING ABOUT.
Hamza says, OKAY, OKAY.
NO OFFENCE, MONSIEUR.
BUT I THINK I'M GOING TO
HAVE THE INVESTIGATORS
CHECK THIS OUT.
Jacques says, WELL, SUIT YOURSELF.
An animated KoolKatt looks through a magnifying glass.
An announcer says, INVESTIGATION.
A young boy and girl appear on a screen.
Hamza says, HI, INVESTIGATORS.
The kids say, HI, HAMZA.
Hamza says, ALEXANDRA, ETHAN,
I HAVE A QUESTION FOR YOU.
A TYPICAL YEAR
HAS 365 DAYS, RIGHT?
Alexandra and Ethan say, YEAH.
RIGHT.
Hamza says, SO, HOW MANY DIFFERENT
BIRTHDAY DATES
COULD THERE BE IN THE YEAR?
Alexandra and Ethan say, 365?
Hamza says, EXACTLY. SO, HOW MANY
PEOPLE DO YOU THINK
YOU'D HAVE TO ASK
BEFORE YOU'D FIND TWO
WITH THE SAME BIRTHDAY?
Alexandra says, WELL, I THINK WE SHOULD
DIVIDE IT IN TWO,
'CAUSE WE NEED
TWO PERSONS.
Ethan says, OR 185?
Alexandra says, YEAH, ABOUT THAT.
Hamza says, YOU KNOW, I THINK IT
WOULD TAKE A LOT OF PEOPLE, TOO.
BUT I HAVE A BUDDY HERE WHO
THINKS YOU'D NEED A LOT LESS.
LET'S TEST IT.
ASK PEOPLE THEIR BIRTHDAYS
UNTIL YOU FIND A MATCH.
Ethan says, WE'RE ON IT.
The kids approach a group of people outside a large grey brick and stone building.
Ethan says, WE'RE DOING A TV SHOW
ON PROBABILITY,
AND WE'RE WONDERING
WHAT YOUR BIRTHDAY IS.
A woman says, THE 14TH OF FEBRUARY.
Alexandra asks, AND WHAT'S
YOUR BIRTHDAY?
A woman says, MARCH 24TH.
Alexandra kneels beside the small white dog and holds a microphone to its face. She asks, WHEN'S YOUR BIRTHDAY?
COME ON, TELL ME.
The dog’s male owner says, HE ONLY
SPEAKS FRENCH.
Alexandra says, OH.
A line graph appears.
A computerized voice says,
ACCORDING TO THE LAWS
OF PROBABILITY,
IN A ROOM WITH 23 PEOPLE,
IT'S MORE THAN 50% CERTAIN
THAT AT LEAST TWO
WILL HAVE THE SAME BIRTHDAY.
WITH 30 PEOPLE IT'S 75%,
AND WITH 70 IT'S 99%.
BY DOING LOTS OF EXPERIMENTS
LIKE THESE,
WE CAN SEE THAT THE LAWS
OF PROBABILITY WORK.
Ethan holds a microphone up to a woman and asks, AND YOU?
The woman says, MAY THE 18TH.
Several women answer Alexandra and Ethan, MAY 26TH.
SEPTEMBER 6TH.
FEBRUARY 22ND.
AUGUST 28TH.
MAY THE 18TH.
Ethan says, WE GOT TWO.
Hamza says, WOW!
Alexandra says, ALL RIGHT.
THANK YOU.
Hamza asks, HOW MANY DID IT TAKE?
Alexandra counts checkmarks on a grid and counts, ONE, TWO, THREE,
FOUR, FIVE, SIX,
SEVEN, EIGHT, NINE,
10, 11, 12, 13.
Ethan says, JUST 13.
Alexandra says, YEAH. A LOT LESS
THAN WE THOUGHT.
Hamza says, THAT'S A LOT LESS
THAN WE BOTH THOUGHT.
WE'LL CATCH UP
WITH THE INVESTIGATORS LATER.
BUT THE PROBABILITY THAT
I'M BLOWN AWAY BY THIS IS 100%.
Jacques says, AHA!
I KNEW HE'D SEE IT MY WAY.
Hamza continues, PROBABILITY SAYS THAT
A COIN SHOULD LAND HEADS
HALF THE TIME, RIGHT?
SO, MAYBE
I'LL JUST STICK TO HEADS,
AND MAYBE KOOL CAT'S COIN
WILL LAND ON HEADS
A BUNCH OF TIMES IN A ROW.
Koolkatt shakes his head.
Jacques says, AH, EXCUSEZ-MOI.
HOLD YOUR HORSES.
UH, YOU'VE FALLEN FOR
THE MONTE CARLO FALLACY.
Jacques plays Go Fish with KoolKatt.
Jacques says, UH--
GO FISH.
Hamza says, THE MONTE CARLO
WHAT-ACY?
Jacques says, FALLACY. IT'S WHEN
SOMETHING IS NOT TRUE.
IN THIS PARTICULAR CASE,
IT IS THE IDEA THAT
IF YOU'VE HAD BAD LUCK,
YOUR LUCK
HAS TO CHANGE.
THE PROBABILITY OF FLIPPING
A COIN TO TAILS 10 TIMES IS--
IT'S SMALL.
BUT THE PROBABILITY
OF EACH INDIVIDUAL FLIP
IS THE EXACT SAME
EVERY TIME YOU FLIP IT.
DO YOU HAVE ANY THREES?
Koolkatt shakes his head.
Hamza says, I GUESS I STILL HAVE A LOT MORE
TO LEARN ABOUT PROBABILITY.
(Upbeat music plays)
Panels of a puzzle shift and become a picture of Koolkat.
A graphic of a cat head with ears inside it appears.
An announcer says, BRAIN BENDER
Hamza says, TODAY'S PUZZLE-SOLVERS
ARE EVAN AND ALYSSA.
HELLO.
Evan and Alyssa wave and say HI, HAMZA.
HI.
Hamza says, OUR BRAIN-BENDER
IS GOING TO BE A BIT DICEY.
YOU SEE A PAIR OF DICE,
RIGHT?
The kids say, YEAH.
Hamza says, THERE ARE 12 CUPS.
EACH CUP REPRESENTS A NUMBER YOU
COULD ROLL WITH A PAIR OF DICE.
HERE'S THE BRAIN-BENDER.
IF YOU ROLL A PAIR OF DICE
A LOT OF TIMES,
WHICH OF THESE 12 NUMBERS
DO YOU THINK
YOU'LL GET MOST OFTEN?
Evan says, FIVE. FOUR, MAYBE.
Hamza says, WELL,
LET'S FIND OUT.
Evan rolls the dice and says, FOUR.
He drops a token into a red and white cup labelled with the number 4.
Alyssa rolls the dice and says, SIX.
She drops a token into a cup labelled with the number 6.
Evan rolls the dice and says, SEVEN. THERE.
Alyssa rolls the dice and says, 10.
She rolls again and says, SEVEN.
SIX AND SEVENS
ARE IN THE LEAD.
The kids roll the dice repeatedly.
Hamza says, IT LOOKS LIKE THEY'RE ON A ROLL.
WE'LL CHECK BACK WITH THEM
LATER.
(BRAKES SQUEALING)
An animation shows blue and yellow KoolKatts racing down a street.
The announcer says, CHALLENGE.
Hamza stands in a park with two teams of one boy and one girl wearing yellow or blue shirts.
He says, WELCOME TO THE
LOOK KOOL
PROBABILITY CARNIVAL.
AND TO MY RIGHT, I HAVE KIKI
AND ZACHARY. TEAM YELLOW.
Kiki and Zacahry say, TEAM YELLOW.
Hamza continues, AND ON MY LEFT, I HAVE
ELENI AND DONATO. TEAM BLUE.
Eleni adn Donato says, TEAM BLUE.
Hamza and the kids approach a game with several picture of KoolKatt wearing a clown hat and nose.
Hamza says, FIRST UP, WE HAVE
THE BALL TOSS.
BUT BE WARNED.
ONE OF THESE CLOWNS
IS THE DREADED CLOWN OF DOOM.
A red mannequin head wears a colorful clown wig.
(EVERYONE GASPING)
Hamza says, MM-HMM. WHOEVER KNOCKS IT OVER
WILL FACE DIRE CONSEQUENCES.
ZACHARY, YOU GET TO GO FIRST.
He throws a ball through one of the KoolKatt pictures. Text over the clown head reads, safe.
Hamza says, OOH. LET'S TAKE A CLOSER LOOK AT
THIS WITH MY MIND'S EYEGLASSES.
Hamza puts on glasses.
A computerized voice says,
NOW THAT ONE OF
THE EIGHT CLOWNS
HAS BEEN ELIMINATED,
THE PROBABILITY OF HITTING
THE CLOWN OF DOOM
BECOMES ONE IN SEVEN.
Hamza removes the glasses and says, WHOA!
NOW IT'S TEAM BLUE'S TURN.
Kids take turns throwing balls at the wall of KoolKatt pictures.
Hamza says, YES.
WOO-HOO-HOO!
The computerized voice says, WITH EVERY SAFE SHOT,
THE DANGER INCREASES.
THE PROBABILITY
IS NOW ONE IN FIVE.
ALL RIGHT, DONATO.
Kids take turns throwing balls at the wall of KoolKatt pictures.
Hamza says, OOH.
KEANA, THE PROBABILITY IS?
Keana says, ONE OUT OF TWO.
Hamza says, ONE OF THESE IS
THE CLOWN OF DOOM.
LET'S FIND OUT WHICH ONE IT IS.
Keana throws a ball and knocks over a picture.
Hamza says, WOO-HOO-HOO!
DONATO, WHAT DO YOU THINK
IS THE PROBABILITY THAT
THAT IS THE CLOWN OF DOOM?
Donato says, ONE OUT OF ONE.
Hamza says, I'M PRETTY SURE
YOU'RE RIGHT.
Donato throws a ball at the last picture. It flips over revealing a picture of a clown.
(SIREN WAILING)
Hamza says, OH! THERE IT IS.
Donato says, UH-UH.
Water sprays Donato from the mouth of the red mannequin head.
He falls over laughing and says, UGH!
Hamza says, WELL, I THINK THE
PROBABILITY OF THIS CHALLENGE
GETTING WETTER IS REALLY HIGH
WHEN WE GET BACK.
Two red water balloons pop.
(EVERYONE CHEERING)
Hamza flips a coin and says, OH, HEADS. IF IT'S HEADS HALF
THE TIME I FLIP THE COIN,
HOW COME KOOL CAT KEEPS WINNING?
OH, WELL. LET'S SEE HOW
THE BRAIN-BENDER IS GOING.
Hamza approaches the screen and waves his hand.
Evan says, THE LAST ROLL
OF THE GAME IS...
Evan rolls the dice.
Evan and Alyssa say, ...FIVE.
Evan drops a token into a cup
He says, OH.
Hamza says, OKAY. IT'S TIME TO COUNT UP
HOW MANY TOKENS ARE IN EACH CUP.
Evan and Alyssa take tokens out of the cups and count,
12, WE HAVE FOUR.
SIX, 10.
THREE, SEVEN AND EIGHT.
WOW. WE GOT A LOT.
15.
IN SIX WE HAVE 13.
IN FIVE WE HAVE SEVEN.
FOUR, FIVE. SIX.
IN TWO, WE ONLY HAVE ONE.
AND IN ONE, NOTHING.
Evan says, YOU KNOW, IT'S ACTUALLY
IMPOSSIBLE TO GET A ONE,
BECAUSE THERE'S TWO DICE.
Hamza says, SO, TELL ME WHICH ONE
ACTUALLY HAD THE MOST.
The kids say, SEVEN.
Hamza says, DO YOU KNOW WHY?
Evan says, NO.
Hamza says, WHY DO YOU THINK
THEY CALL IT
LUCKY NUMBER SEVEN?
Evan says, MAYBE BECAUSE SEVEN ALWAYS WINS.
Alyssa says, A REALLY GOOD ANSWER,
I THINK.
Hamza says, PROBABLY.
THANKS, EVAN. THANKS, ALYSSA.
Evan and Alyssa wave and say, BYE, HAMZA.
BYE.
Evan rolls two yellow and orange dice and says,
THERE YOU GO. SEVEN.
I'M GOING TO SEE IF THERE'S
A MATHEMATICAL EXPLANATION
BEHIND "LUCKY SEVEN."
IF I HAVE TWO DICE,
HOW MANY DIFFERENT WAYS
CAN I ROLL SEVEN?
The animation of KoolKatt breaks into multiple pieces then reforms whole.
The announcer says, DECONSTRUCT.
Hamza says, DECONSTRUCT.
WHOA.
The dice float in mid air, rotating into various combinations of seven.
Hamza says, ARE YOU SEEING WHAT I'M SEEING?
THERE ARE A LOT OF POSSIBLE
COMBINATIONS TO MAKE SEVEN.
A graphic appears showing all possible dice combinations.
Hamza says, OH, AND LOOK.
THERE'S A PATTERN
TO THE COMBINATIONS.
THERE'S ONE WAY TO MAKE TWO,
TWO WAYS TO MAKE THREE,
THREE WAYS TO MAKE FOUR,
FOUR WAYS TO MAKE FIVE,
FIVE WAYS TO MAKE SIX,
AND SIX WAYS TO MAKE SEVEN.
THE NUMBER OF POSSIBILITIES
INCREASES BY ONE
UNTIL YOU GET
TO SEVEN.
AND THEN IT DECREASES
FOR EVERY NUMBER AFTER THAT
UNTIL YOU GET TO 12.
HEY, IT MAKES A TRIANGLE.
SO, "LUCKY SEVEN"
IS ACTUALLY JUST
THE MOST LIKELY NUMBER
THAT YOU CAN ROLL WITH TWO DICE.
IT'S NOT REALLY LUCK AT ALL.
The 4-leaf clover walks and smiles.
He says, OH, BOY. I FEEL LUCKY TODAY.
UH-OH.
(THUNDER CRASHING)
Rain falls on the clover, then lightning strikes it.
The clover lies on the ground and says, WELL, I GUESS I SHOULDN'T HAVE
CARRIED THIS BIG HUNK OF METAL
IN A THUNDERSTORM.
OH, NO.
Lightning strikes the horseshoe. The horseshoe falls on the clover.
The clover says, OH, MAN.
The animated KoolKatt looks through the magnifying glass.
The announcer says, INVESTIGATION.
A woman says, MY BIRTHDAY IS NOVEMBER 21ST.
Ethan and Alexandra chase after a pigeon.
They yell, WHEN'S YOUR BIRTHDAY?
NO, DON'T GO. WAIT!
A man says, NOVEMBER 16TH.
Ethan says, AND YOU?
Several people respond, NOVEMBER 9TH.
10TH OF MARCH.
22ND OF NOVEMBER.
MINE IS NOVEMBER 9TH.
Alexandra says, OH, WE HAVE A MATCH.
Hamza says, OKAY.
HOW MANY PEOPLE DID IT TAKE
TO GET A BIRTHDAY MATCH
THIS TIME?
Alexandra says, 37.
THAT'S NOT A LOT...
Ethan says, ...COMPARED TO
WHAT WE THOUGHT.
Alexandra says, YEAH. 180 COMPARED TO 37?
THAT'S NOTHING.
Hamza says, NEITHER TRY TOOK 180 PEOPLE.
Ethan and Alexandra say,
NO.
NOT EVEN CLOSE.
The line graph appears.
The computerized voice says, THE PROBABILITY
OF FINDING A MATCH
AFTER ASKING 13 PEOPLE
IS ONLY 19%.
THAT IS SOMEWHAT UNLIKELY.
THE PROBABILITY
OF FINDING A MATCH
AFTER 37 PEOPLE IS 85%.
VERY LIKELY.
AFTER ASKING ONLY 60 PEOPLE,
YOU ARE ALMOST CERTAIN
TO HAVE A MATCH.
Hamza says, THE NUMBER OF PEOPLE
IS A LOT LOWER
THAN WE THOUGHT.
READY TO DO
SOME ROCKET SCIENCE NOW?
Ethan says, YEAH.
Alexandra says, OH, YEAH. BIG TIME.
The animated sun rises.
Vanessa says, WELCOME BACK.
I HOPE YOU ENJOYED THE VIDEO.
The caption reads, Junior 4-6. Teacher Vanessa.
She continues, WE'RE GOING TO TALK ABOUT
THE ODDS
OF MULTIPLE EVENTS HAPPENING.
SO, YOU SEE TO MY RIGHT HERE,
OR YOUR LEFT,
THREE DIFFERENT SPINNERS.
AND WE HAD JUST TALKED ABOUT
THEORETICAL PROBABILITY
BEING THE NUMBER OF
LIKELY EVENTS
OVER THE TOTAL POSSIBILITY
OF EVENTS THAT COULD HAPPEN.
SO, IF WE LOOK FIRST
ON THIS SPINNER,
IF I WANTED TO LAND ON
ONE OF THE SIDES OF THE SPINNER,
I'D HAVE A PROBABILITY
OF ONE OVER TWO.
OKAY? SO, I COULD EITHER LAND
HERE OR I COULD LAND HERE.
Vanessa points at a circle divided into two sections.
She continues, THAT MEANS I HAVE
AN EQUALLY LIKELY PROBABILITY
THAT I'D LAND ON THE BLUE SIDE
Vanessa colors half the circle blue.
COMPARED TO LANDING ON
THE WHITE SIDE.
EQUALLY LIKELY.
IN THE MIDDLE SPINNER, I HAVE
ONE, TWO, THREE, FOUR SECTIONS.
SO, THE ODDS OF ME LANDING ON
ANY ONE OF THOSE FOUR SECTIONS
IS ONE OUT OF FOUR.
AND ON THE SPINNER HERE,
WE SEE THAT WE HAVE
ONE, TWO, THREE, FOUR,
FIVE, SIX.
SO, THE LIKELIHOOD OF ME LANDING
ON ANY ONE OF THOSE SECTIONS
OF THE SPINNER IS ONE OVER SIX.
OKAY? SO, AS YOU SEE,
YOUR ODDS OF LANDING ON
ANY ONE SECTION
GET SMALLER, EVEN THOUGH
THE FRACTION GETS BIGGER.
THE PERCENT GETS SMALLER
AS YOU HAVE MORE SECTIONS ADDED.
Vanessa removes the drawings of circular spinners from the tabletop display.
A new sheet reads, Red twice in a row: 1/4 x 1/4.
Vanessa continues, SO, WHAT HAPPENS IF ONE OF
YOUR FRIENDS AND YOURSELF
PLAY A GAME,
AND YOU ARE SPINNING
A WHEEL,
AND YOU HAVE FOUR SECTIONS.
AND THE WAY TO WIN IS IF
YOU LAND ON RED TWICE IN A ROW.
WHAT ARE YOUR ODDS
OF WINNING THE GAME?
OKAY?
SO, WE KNOW THAT WE HAVE
A ONE-OUT-OF-FOUR PROBABILITY
OF WINNING,
BECAUSE WE KNOW WE HAVE ONE RED
OUT OF A TOTAL OF FOUR.
OKAY? SO, AFTER ONE SPIN,
THAT'S THE PROBABILITY.
WHAT ARE THE ODDS
THAT YOU CAN GET IT TWICE?
SO, ON YOUR SECOND SPIN,
YOU AGAIN HAVE
A ONE-OUT-OF-FOUR PROBABILITY
OF YOU SPINNING A RED.
IN TOTAL,
TO FIND OUT WHAT OUR PROBABILITY
WOULD BE
FOR THESE TWO EVENTS HAPPENING
AFTER EACH OTHER,
WE CAN MULTIPLY
THE TWO FRACTIONS TOGETHER.
SO, WHEN WE MULTIPLY FRACTIONS,
WE LOOK TO MULTIPLY
THE NUMERATORS.
ONE TIMES ONE IS ONE.
AND WE PUT IT OVER
THE DENOMINATOR.
SO, WE MULTIPLY THOSE TWO
TOGETHER.
FOUR TIMES FOUR IS 16.
Vanessa writes the fraction 1/16.
She says, SO, MY ODDS OF ROLLING RED
TWICE IN A ROW
ON THIS WHEEL
ARE ONE OUT OF 16.
NOW, IF I'M PUTTING THAT ON
MY NUMBER LINE,
I KNOW THAT IT WOULD BE
ALMOST BETWEEN
IMPOSSIBLE AND UNLIKELY.
OKAY?
Vanessa points at the number line.
She says, SO, THIS IS A HARD GAME TO WIN,
TO GET TO ROLL--
OR TO SPIN RED TWICE IN A ROW.
BUT LET ME TRY, 'CAUSE I THINK
I WAS LUCKY ON THAT OTHER.
(LAUGHING)
THAT OTHER GAME.
I WAS PICKING A HEART. OKAY.
Vanessa spins the 4-colored lazy Susan wheel.
SO, UNFORTUNATELY, NO.
I ROLLED WHITE.
AND I ROLLED WHITE AGAIN.
SO, I WOULD NOT HAVE WON
ON MY GAME.
THE ODDS OF ME LOSING, THEN,
WOULD BE--
SO, THIS IS FOR A WIN.
AND THEN WE KNOW THAT
MY ODDS OF LOSING
WOULD BE 15 OUT OF 16.
SO, MUCH HIGHER
THAT I WOULD'VE LOST.
BECAUSE WE KNOW 15 OVER 16
PLUS ONE OVER 16
GIVES ME 16 OVER 16, OR A WHOLE.
OKAY? SO, UNFORTUNATELY,
I DIDN'T WIN THAT GAME.
Vanessa reveals a new sheet of paper on the display that reads, 3 heads in a row: 1/2 x 1/2 x 1/2
Vanessa continues, NOW, WHAT IF SOMEONE SAYS,
"CAN YOU FLIP A COIN
"SO THAT YOU GET HEADS
THREE TIMES IN A ROW?"
WELL, WHAT'S THAT PROBABILITY?
SO, ON THE FIRST ROLL,
I HAVE A ONE-IN-TWO SHOT,
BECAUSE WE TALKED ABOUT
HEADS OR TAILS
BEING THE TWO POSSIBILITIES,
AND WE SAID WE WANTED HEADS,
OKAY?
SO, THAT WOULD BE MY FIRST ROLL,
MY FIRST FLIP.
MY SECOND FLIP,
I HAVE THE SAME PROBABILITY.
AND MY THIRD FLIP, I HAVE TO GET
A ONE-OUT-OF-TWO SHOT
OF GETTING A HEAD.
WHAT IS THAT ALTOGETHER?
SO, WE CAN MULTIPLY
OUR FRACTIONS.
ONE TIMES ONE TIMES ONE,
YOU GET ONE.
OVER-- NOW, WE MULTIPLY
OUR DENOMINATORS TOGETHER.
TWO TIMES TWO IS FOUR.
TIMES TWO AGAIN IS EIGHT.
Vanessa writes the fraction 1/8.
She says, SO, I HAVE A ONE-OUT-OF-EIGHT
PROBABILITY
OF FLIPPING A COIN AND
RECEIVING HEADS, THREE IN A ROW.
THREE TIMES IN A ROW.
AGAIN, WE'RE LOOKING AT
THE "UNLIKELY" RANGE.
UM, SOMEWHERE IN BETWEEN HERE.
OKAY? SO, YOUR FRIEND
IS MORE LIKELY TO WIN
IF THEY SAID THAT
THEY COULD ROLL ANYTHING
BUT THREE HEADS IN A ROW.
IF THEY SAID THAT THEY COULD
ROLL EITHER A HEADS OR TAILS?
(LAUGHING)
AH, THAT WOULD BE SMART.
OKAY. SO, LET'S SEE IF I CAN
ROLL THREE HEADS IN A ROW.
Vanessa flips a coin and says,
ONCE, AND I PROMISE
I'M NOT CHEATING.
CAN YOU SEE THE REFLECTION?
OKAY.
She flips the coin again and says, NO. I GOT A TAIL.
OKAY? SO, I DIDN'T WIN AGAIN.
AND HOW DO WE KNOW THAT
IT WAS GOING TO BE DIFFICULT
FOR ME TO WIN THIS GAME?
BECAUSE WHEN WE PLOT IT
ON OUR NUMBER LINE,
WE SEE THAT ONE OUT OF EIGHT
IS A VERY SMALL FRACTION,
LESS THAN UNLIKELY.
SO, THAT GAME WOULD BE
VERY, VERY DIFFICULT TO WIN.
LET'S PLAY ONE MORE BEFORE
WE WATCH OUR NEXT EPISODE
OF
MATHXPLOSION.
Vanessa picks up a deck of cards and places a blue card with the fraction 26/52 on the display.
Vanessa says, UM, LET'S SEE IF I CAN
GET THESE ODDS HERE.
SO, WHAT DO YOU THINK
I'M GOING TO--
HOW CAN I WIN THIS GAME?
LET'S SAY I CAN PICK EITHER
TWO OF TWO DIFFERENT SUITS,
OR I COULD PICK, UM,
ONE RED CARD.
OKAY? SO, I KNOW THAT THERE ARE
26 RED CARDS IN THIS DECK.
AND THERE'S 26 BLACK CARDS
IN THIS DECK,
SO IT'S EQUALLY LIKELY THAT
I WOULD PICK A RED OR A BLACK.
SO, MY CHANCES ARE RIGHT IN
THE MIDDLE OF THAT NUMBER LINE,
THAT 0.5, OR ONE OVER TWO.
UM, LET'S GO THIS WAY.
ACTUALLY, NO. LET'S TRY IT.
LET'S DO IT THIS WAY AGAIN.
OKAY. SO, LET'S SEE MY ODDS OF
PICKING A BLACK CARD
ON THE TOP OF MY PILE.
Vanessa picks the 8 of hearts out of the deck.
Vanessa says, AND IT WAS A RED.
SO, UNFORTUNATELY, I DID NOT WIN
THE GAME
THAT I WOULD HAVE WON
IF I HAD DRAWN A BLACK CARD.
SO, I WAS EQUALLY LIKELY
TO WIN AND LOSE,
AND UNFORTUNATELY,
I TAKE THE LOSS ON THIS ONE.
SO, I WOULD LOVE FOR YOU TO
WATCH THIS NEXT EPISODE
OF
MATHXPLOSION.
IT'S GOING TO TEACH YOU
HOW SOCKS AND MATH TOGETHER
ARE AN AWESOME, AWESOME
MAGIC TRICK.
SO, CHECK IT OUT, AND I'LL
MEET YOU HERE AFTER THE VIDEO.
The animated sun rises.
(laser sounds)
Kids sing, WHAT A HIT
IT'S NOT A TRICK
IT'S
MATHXPLOSION
The MathXplosion logo appears.
The kids sing, JUST FOR YOU, COOL AND NEW
MATHXPLOSION
A brown-haired man with a neatly trimmed beard, carries a brown wooden drawer full of colorful socks.
He wears a red t-shirt with the MathXplosion logo on it.
The man says, DID YOU KNOW THAT I CAN FIND
TWO SOCKS OF THE SAME COLOUR
IN THIS MESSY SOCK DRAWER
WITH MY EYES CLOSED?
YEP, THAT'S RIGHT.
AND AS AMAZING
AS THAT SOUNDS ALREADY,
I NEED TO PICK
JUST FOUR SOCKS TO DO IT.
I'LL SHOW YOU HOW IT'S DONE.
YOU WON'T BELIEVE YOUR EYES.
The man opens the drawer. It is empty.
The man says, NEED SOME SOCKS, PLEASE.
GET SOME SOCKS.
The man stands behind a table.
I HAVE BEFORE ME
A DRAWER FULL OF SOCKS.
THESE SOCKS COME IN
THREE DIFFERENT COLOURS.
WE HAVE BLUE, GREEN AND PINK.
THE TOTAL NUMBER OF SOCKS
IN THE DRAWER
DOESN'T MATTER AT ALL,
AS LONG AS I KNOW
HOW MANY COLOURS THERE ARE.
IN THIS CASE, THREE COLOURS.
SO, WHAT I'M GOING TO DO IS
PULL JUST FOUR SOCKS
FROM THE DRAWER IN THE DARK.
AND I CAN GUARANTEE
THAT AT LEAST TWO
WILL BE OF THE SAME COLOUR.
LET'S TURN OFF THESE LIGHTS.
(CLAPPING)
GREAT. OH, BOY. THAT'S DARK.
(CAT YOWLING)
OH, SORRY, KITTY.
OKAY.
YOU KNOW, THIS IS WAY TOO DARK.
THIS ISN'T WORKING.
LET'S TURN THE LIGHTS BACK ON.
(CLAPPING)
LIGHTS?
(CLAPPING)
OH.
WELL, THAT DIDN'T WORK AT ALL.
(CHUCKLING)
I KNOW.
I'LL DO THIS BLINDFOLDED.
OKAY.
The man puts on a blindfold, then reaches into the drawer and pulls out socks.
He says, ONE, TWO, THREE.
ANY MATCHING COLOURS YET?
NO?
OKAY.
WELL, KEEP YOUR EYE ON
SOCK NUMBER...
...FOUR.
The man pulls out a second pink sock and says,
YES.
THE FIRST THREE SOCKS
WERE DIFFERENT COLOURS,
SO THE FOURTH ONE
HAS
TO MATCH.
IF YOU START WITH
THREE SOCK COLOURS,
PICKING FOUR SOCKS
GUARANTEES AT LEAST TWO SOCKS
OF THE SAME COLOUR.
AMAZING.
The man draws a yellow circle on a chalkboard, then taps the circle with his fist. The chalkboard becomes a monitor showing an animation of socks floating out of a dresser drawer.
The man says, THE LIKELIHOOD OF SOMETHING
HAPPENING,
LIKE CHOOSING
A SPECIFIC SOCK COLOUR,
IS CALLED PROBABILITY.
YOU CAN USE
THE SAME TRICK ON MITTENS, TOO.
TO GUARANTEE THAT YOU
FIND TWO MITTENS
OF THE SAME COLOUR IN THE DARK,
THE NUMBER OF MITTENS TO PICK UP
IS THE NUMBER OF MITTEN COLOURS
PLUS ONE.
THREE COLOURS, FOUR MITTENS.
Four mittens float above the dresser.
The man says, SO, THERE YOU HAVE IT.
I'VE SHARED YET ANOTHER
AMAZING SECRET:
HOW TO MATCH UP SOCKS
IN THE DARK.
TRY IT OUT YOURSELVES AT HOME.
BUT REMEMBER, USE CLEAN SOCKS.
(SNIFFING)
NOT SMELLY ONES.
PROBABILITY.
IT'S NOT MAGIC; IT'S MATH.
The drawer is full of socks. The Math Xplosion logo appears.
Text reads, produced by GAPC Entertainment. In association with TVO Kids. With the financial participation of Bell Fund, Canadian Media Fund and Shaw Rocket Fund.
The animated sun rises.
Vanessa says, WELCOME BACK.
LET'S PUT IT ALL TOGETHER NOW.
REVIEWING OUR DEFINITION
OF PROBABILITY,
THE LIKELIHOOD
OF SOMETHING HAPPENING.
WE'VE SHOWN IT THROUGH
A FRACTION AND NUMBER LINE.
AND WE USE PROBABILITY TO
MAKE DECISIONS AND PREDICTIONS,
ESPECIALLY THE WEATHER.
SO, THIS IS THE TIME FOR YOU
TO GET INVOLVED.
IF YOU HAVE THOSE MARKERS
AND THAT PAPER
AND DIFFERENT FORMS OF
PROBABILITY GAMES,
I WOULD LOVE FOR YOU
TO GET THAT READY
AND BRING IT TO YOUR WORK AREA.
AND WE ARE GOING TO
PLAY A LITTLE GAME.
SO, YOU, ON A PIECE OF PAPER,
WILL WRITE PROBABILITY EVENTS
THAT COULD HAPPEN IN WORDS.
OKAY?
SO, FOR EXAMPLE...
Vanessa places a green card on the tabletop display. It reads, “I win the lottery”.
Vanessa continues, ...MY FIRST POSSIBLE EVENT
THAT COULD HAPPEN?
I WIN THE LOTTERY.
OKAY? SO, I'M PICKING AN EVENT
THAT COULD HAPPEN.
AND THEN,
WHAT I'M GOING TO DO IS
THINK ABOUT THE LIKELIHOOD
OF IT OCCURRING. OKAY?
SO, YOU COULD THEN EXCHANGE
YOUR EVENT WITH A FRIEND,
MAYBE WITH A PARENT.
MAYBE TALK TO, UM,
ANOTHER ADULT IN YOUR LIFE,
LIKE A TEACHER.
ASK THEM WHAT ARE THE ODDS THAT
THEY'RE GOING TO WIN THE LOTTERY
THIS WEEK, AND THEN
PLOT IT ON YOUR NUMBER LINE.
Vanessa holds up the number line.
She continues, SO, IF I SAID TO MY TEACHER,
"MISTER OR MISS,
WHAT ARE THE ODDS
THAT YOU'RE GOING TO WIN
THE LOTTERY THIS WEEK?"
YOU CAN TELL THEM THAT,
IF THEY'RE UNSURE,
THAT IT WOULD BE SOMEWHERE
IN THIS RANGE
THAT THEY WIN THE LOTTERY.
OKAY? SO, THIS EVENT,
WE KNOW THAT OCCURS--
ONE OUT OF 33,000,000
ARE THE ODDS
OF WINNING THE LOTTERY.
SO, VERY, VERY UNLIKELY
THAT YOU WIN THE LOTTERY.
YOU COULD COME UP WITH
ANOTHER EVENT
THAT YOU COULD ASK YOUR FRIEND
MIGHT HAPPEN.
YOU FLIP A COIN
AND YOU LAND ON TAILS.
NOW, KNOWING WHAT YOU DO
ABOUT PROBABILITY,
YOU KNOW THAT YOU HAVE
AN EQUALLY LIKELY PROBABILITY,
ONE OVER TWO, BECAUSE TAILS--
THERE'S EITHER HEADS OR TAILS
AS THE POSSIBLE OUTCOMES,
AND YOU LAND ON TAILS.
SO, YOU'RE EQUALLY LIKELY, 50%.
AND THEN, WITH YOUR FRIEND
OR YOUR GUARDIAN OR PARENT,
THEY COULD PLOT THIS
ON THE NUMBER LINE.
I FLIP A COIN AND LAND ON TAILS.
NOW, YOU MIGHT WANT TO GET
SOME CERTAIN ONES IN THERE, TOO.
WE ALL ARE HOPING FOR THIS:
SUMMER WILL COME.
SO, YOU MAKE THAT EVENT
ON A PIECE OF PAPER.
YOU WRITE IT DOWN,
AND YOU ASK YOUR FRIEND,
"WHERE CAN IT BE PLACED
ON THE NUMBER LINE?"
IS THAT IMPOSSIBLE,
EQUALLY LIKELY, OR CERTAIN?
AND WE KNOW CERTAINLY,
EVERY SEASON
COMES WITHIN THE YEAR.
SO, IT'S CERTAIN THAT
THE SUMMER WILL COME,
AND THAT SUMMER BREAK
IS INEVITABLE.
OKAY? SO, WHAT WE'RE PRACTISING
WHEN WE DO THIS GAME,
WE'RE TALKING ABOUT
THE PROBABILITY
OF LIFE EVENTS HAPPENING.
AND ON OUR NUMBER LINE,
WE'RE PLOTTING THEM ON A SCALE
BETWEEN ZERO, HALF, AND ONE
AS OUR BENCHMARK NUMBERS.
OKAY? SO, THIS IS GETTING US
IN THE FRAME OF MIND
OF USING THESE TERMS
THAT WE'RE TALKING ABOUT,
PROBABILITY OF EVENTS.
Vanessa puts a green card on the display that reads, viewers are in grades 4, 5, and 6!
Vanessa says, OUR VIEWERS HERE
ARE IN GRADES 4, 5 AND 6.
THAT IS ALMOST CERTAIN.
OUR KEY DEMOGRAPHIC
FOR THIS VIDEO,
THE CURRICULUM,
IS IN THE JUNIOR GRADES.
SO, ALMOST CERTAINLY,
MANY OF OUR VIEWERS ARE--
MOST OF OUR VIEWERS
ARE, UM, IN THOSE GRADES.
BETWEEN LIKELY AND CERTAIN.
AND FINALLY, FOR A LAUGH,
"I LEARN HOW TO SKATEBOARD."
SO, KNOWING ME, I--
VERY HARD FOR ME TO LEARN THAT
AT MY AGE.
SO, THIS WOULD BE SOMETHING
THAT'S UNLIKELY
THAT I WOULD LEARN HOW TO DO.
SO, IF YOU KNEW SOMETHING ABOUT
YOUR FRIEND,
MAYBE THEY WOULD SAY,
"YOUR FAVOURITE FOOD IS CHIPS,"
FOR EXAMPLE.
AND YOU WOULD SAY,
"YOU KNOW WHAT? IT CERTAINLY IS.
YOU GOT THOSE ODDS RIGHT ON."
SO, YOU CAN WRITE
DIFFERENT LIFE EVENTS
AND SHARE THEM WITH A PARTNER
OR YOUR PARENTS
AND SEE WHERE THEY FALL
ON THE NUMBER LINE.
FOR YOUR SECOND GAME,
Vanessa puts a sheet of paper on the tabletop display.
She says, I WOULD LOVE FOR YOU TO USE
EITHER PLAYING CARDS,
SPINNERS, OR A DIE,
AND HONESTLY,
ALL CAN BE HOMEMADE
WITHIN A FEW MINUTES.
AND YOU'RE GOING TO STATE
A PROBABILITY TO WIN.
SO, IF I SAID I WANT TO MAKE
A GAME
THAT HAS A ONE-IN-FOUR
PROBABILITY TO WIN,
I WOULD MAKE A SPINNER
WITH FOUR SECTIONS ON IT.
IF I SAID I WANTED TO MAKE
A SPINNER--
OR SORRY, A GAME WITH A SPINNER
THAT HAS A PROBABILITY OF ONE
OUT OF SIX AFTER EVERY SPIN,
WE COULD MAKE A SPINNER
LIKE THIS ONE HERE
THAT HAS SIX SECTIONS.
OKAY? SO, IT'S UP TO YOU.
YOU CAN CHOOSE EITHER A SPINNER,
PLAYING CARDS, A DICE, COINS.
WHAT KIND OF GAME
WOULD YOU LIKE TO CREATE?
SO, FOR MY DICE GAME
THAT WE'RE GOING TO PLAY
A LITTLE BIT LATER,
IT'S CALLED MULTIPLY TO WIN.
I'M GOING TO ROLL MY TWO DICE,
AND THE ONLY WAY I CAN WIN
IS IF I ROLL TWO--
THE PRODUCT OF THE TWO ROLLS
HAS TO BE 36.
WHAT DOES THAT MEAN?
HOW CAN I GET 36
WHEN I MULTIPLY
MY TWO ROLLS TOGETHER?
IT MEANS THAT I'D HAVE TO HAVE
MY FIRST DICE, ROLL A SIX,
AND MY SECOND DICE,
ALSO ROLL A SIX.
Two brown dice sit on the table in front of Vanessa.
She says, BECAUSE SIX TIMES SIX
GIVES ME A PRODUCT OF 36.
WHAT ARE THE ODDS OF GETTING 36
AS MY PRODUCT?
WELL, I KNOW I HAVE
A ONE-OUT-OF-SIX CHANCE
OF ROLLING A SIX ON A DICE,
ON A SIX-SIDED DICE.
I ALSO AGAIN HAVE
A ONE-OUT-OF-SIX PROBABILITY
OF ROLLING A SIX
ON MY SECOND ROLL,
BECAUSE IT'S A SIX-SIDED DICE
DOWN HERE
AND THE NUMBER SIX
ONLY OCCURS ONE TIME.
WHEN I MULTIPLY
THOSE TWO NUMBERS TOGETHER,
ONE TIMES ONE IS ONE.
I MULTIPLY MY DENOMINATORS
TOGETHER.
SIX TIMES SIX IS 36.
SO, MY PROBABILITY
OF WINNING MY GAME
IS ONE OUT OF 36.
NOW, IF AGAIN, WE'RE USING IT
ON A NUMBER LINE,
I CAN SEE THAT
IT'S QUITE UNLIKELY
THAT I WILL WIN THIS GAME,
BUT WHY NOT HAVE FUN AND TRY?
SO, GO AHEAD
AND MAKE YOUR OWN GAME,
WHATEVER YOU CHOOSE,
WHATEVER YOU'D LIKE YOUR
PROBABILITY TO BE.
AND PLAY IT WITH A FRIEND,
A SIBLING, A PARENT, A GUARDIAN,
AND LET ME KNOW
HOW MUCH FUN YOU'RE HAVING.
The animated sun rises.
Vanessa continues, HOW ARE THE GAMES GOING?
ARE YOU HAVING A LOT OF FUN?
LET'S TRY MINE.
SO, WE HAD TALKED ABOUT
THEORETICAL PROBABILITY
BEING THE NUMBER OF FAVOURABLE
OUTCOMES
OVER THE NUMBER
OF POSSIBLE OUTCOMES.
AND WE KNOW IN MY GAME,
I REQUIRE BOTH NUMBERS
TO BE SIX,
SO THAT THEY MULTIPLY TO
A PRODUCT OF 36.
SO, I HAVE A ONE-IN-36
PROBABILITY
OF ME WINNING MY GAME.
SO, IT'S NOT VERY LIKELY,
BUT WHY NOT HAVE
A LOT OF FUN DOING IT?
SO, I'M GOING TO ROLL
MY FIRST DICE.
LET'S SEE WHAT I GET
AS MY FIRST.
Vanessa rolls a die and says, I GET A FIVE.
SO, UNFORTUNATELY,
I KNOW THAT NO MULTIPLICATION,
NO PRODUCT WITH A FIVE,
WILL EQUAL 36.
SO, I DIDN'T WIN
THAT FIRST TIME.
LET'S TRY IT AGAIN.
Vanessa rolls the die and says,
I GOT A FOUR.
SO AGAIN, UNFORTUNATELY,
I DIDN'T WIN.
BUT THE PROBABILITY TOLD ME
THAT IT'S VERY UNLIKELY
THAT I WOULD WIN.
OKAY? SO, I CAN MAKE A DECISION
BASED ON HOW LIKELY THE OUTCOME
IS TO HAPPEN GOING FORWARD.
SO, MAYBE AGAIN,
IF I WANTED TO REALLY BEAT
MY FRIENDS,
I COULD SAY, "YOU KNOW WHAT?
IF YOU ROLL TWO SIXES,
YOU CAN WIN," 'CAUSE I KNOW THAT
IT'S VERY, VERY DIFFICULT
FOR THEM TO WIN,
TO ROLL TWO SIXES.
SO, YOU CAN HAVE A LOT OF FUN
WITH YOUR FRIENDS THAT WAY, TOO.
AGAIN, WE'RE GOING TO USE
PROBABILITY IN OUR LIVES
TO MAKE DECISIONS
AND PREDICTIONS.
IF WE KNOW THAT THERE'S
A 10% CHANCE OF RAIN,
WE KNOW THAT IT'S VERY UNLIKELY
THAT YOU HAVE TO BRING
THAT UMBRELLA TO SCHOOL
THAT DAY.
COMPARED TO A 90% CHANCE
OF RAIN,
WHERE IT'S ALMOST CERTAIN
TO RAIN,
YOU'RE GOING TO NEED TO MAKE
A CHANGE OF PLAN
AND PACK THAT UMBRELLA
INTO THAT BACKPACK
BEFORE YOU GET IT--
AS YOU GO OFF TO SCHOOL.
Vanessa holds up the number line.
She says, USING THAT NUMBER LINE,
PLOTTING FROM IMPOSSIBLE
OR NEVER
ALL THE WAY TO CERTAIN, OKAY,
THIS IS GOING TO HELP YOU
UNDERSTAND
HOW LIKELY AN EVENT WILL OCCUR.
IN TERMS OF GAMES,
IN TERMS OF YOUR FAVOURITE TEAM
WINNING THE STANLEY CUP,
THEY'RE ALL EQUALLY AS LIKELY
TO WIN
AT THE BEGINNING OF THE SEASON.
The caption appears that reads, Junior 4-6. Teacher Vanessa.
Vanessa says, I HOPE YOU HAD A LOT OF FUN
WITH TODAY'S EPISODE.
I KNOW I DID. KEEP PRACTISING
THOSE POSITIVE AFFIRMATIONS.
KEEP PRACTISING
USING PHYSICAL ACTIVITY
AS A WARMUP TO GET YOU READY
FOR LEARNING AND EXPLORING,
AND I'LL CATCH YOU NEXT TIME
ON ANOTHER EPISODE
OF
TVOKIDS POWER HOUR
OF LEARNING.
(soft upbeat music plays)
Text reads, TVO kids would like to thank all the teachers involved in the Power Hour of learning as they continue to teach children of Ontario from their homes.
TVO Kids Power Hour of Learning. TVO. Copyright, The Ontario Educational Communications Authority 2021
A title screen over a blue sky reads, Today’s Junior Lesson: Predicting Through Probability.
A female announcer says,
WELCOME TO
TVOKIDS POWER HOUR
OF LEARNING.
A brown haired woman wearing glasses and a leopard print shirt, sits at a table in her home.
A black and white photograph of downtown Toronto hangs on the wall behind her.
The woman says, HELLO, STUDENTS. HOW ARE YOU?
WELCOME TO ANOTHER EPISODE OF
TVOKIDS POWER HOUR OF LEARNING.
A caption appears that reads, Junior 4-6. Teacher Vanessa.
The woman continues, MY NAME IS TEACHER VANESSA,
AND I'M SO EXCITED TO SPEND
THE NEXT 60 MINUTES TOGETHER
LEARNING, HAVING A LOT OF FUN,
AND SHARING A FEW LAUGHS
TOGETHER.
BUT BEFORE WE BEGIN,
I'M HOPING THAT
YOU'VE BEEN PRACTISING
OUR POSITIVE AFFIRMATIONS THAT
WE LEARNED A FEW WEEKS AGO.
THESE ARE POSITIVE STATEMENTS
CALLED MANTRAS,
AND THEY HELP US BUILD
OUR SELF-CONFIDENCE
BY REPEATING THEM
OVER AND OVER EACH DAY.
SO, I'M GOING TO TELL YOU
OUR THREE MANTRAS,
AND I WOULD LOVE FOR YOU
TO REPEAT AFTER ME.
ARE YOU READY?
I AM CAPABLE.
LET ME HEAR YOU.
Vanessa holds her hand to her ear.
I AM A MATH PERSON.
GOOD JOB. AND I CAN DO IT.
AWESOME. I CAN HEAR YOU
ALL THE WAY FROM STONEY CREEK.
SO, TODAY WE'RE GOING TO BE
TALKING ABOUT PROBABILITY.
WHAT ARE THE ODDS
OF SOMETHING HAPPENING?
AND BEFORE WE BEGIN,
I WAS THINKING THAT
I COULD BRING MY SON CHASE OUT
TO PLAY A PROBABILITY GAME
AND GET US WARMED UP
FOR SOME GREAT LEARNING
OVER THE NEXT HOUR.
A young brown-haired boy, Chase, hops behind Vanessa. He wears a black T-shirt
Vanessa says, WELCOME, CHASE.
COME ON IN.
SO, WHAT WE'RE GOING TO
BE DOING--
JUST STAND BESIDE ME,
RIGHT HERE.
RIGHT HERE,
ON THE TABLE.
ARE YOU READY TO PLAY
A MATH GAME?
A caption reads, Junior 4-6. Chase.
Chase says, YEAH!
Vanessa says, OKAY. SO, STAND UP
NICE AND STRAIGHT
SO EVERYBODY
CAN SEE YOU.
OKAY. SO, I AM GOING TO
ROLL A DICE,
AND WHATEVER NUMBER
WE LAND ON,
THAT'S HOW MANY
EXERCISES--
YEAH. ARE YOU READY
TO SHOW THE KIDS
SOME EXERCISES?
SO, BEFORE YOU BEGIN,
MAKE SURE THAT YOU HAVE
A BIG SPACE
TO DO SOME EXERCISES,
JUST LIKE CHASE IS.
MAKE SURE
YOU CAN SPREAD OUT
AND HAVE A LOT
OF ROOM.
SO, WE'RE GOING TO
GET OUR BODIES READY
SO THAT OUR MINDS
WILL BE READY TO LEARN.
I'M GOING TO ROLL
THE FIRST DICE,
AND IT LANDS ON
A FOUR.
Vanessa holds up a large die made of brown cardboard paper.
Vanessa says, SO, CHASE, DO YOU MIND
DOING FOUR JUMPING JACKS?
Chase does jumping jacks and counts, OKAY. ONE, TWO, THREE, FOUR.
Vanessa says, AWESOME. NEXT ROLL.
Vanessa rolls the die and says, A ONE. HOW ABOUT YOU DO
ONE NECK CIRCLE?
Chase and Vanessa do a neck circle.
Vanessa says, NEXT ROLL, WE HAVE
A ONE AGAIN.
HOW ABOUT ONE HIGH KNEE?
Chase raises his left knee.
Vanessa says, OKAY. LAST ROLL.
ARE YOU READY?
Chase says, YEAH.
Vanessa rolls the die and says, SIX. LET'S DO
SIX ARM CIRCLES
TO GET OUR ARMS READY TO
WRITE AND PLAY SOME GAMES.
Chase circles his arms and counts, ONE, TWO, THREE, FOUR,
FIVE, SIX.
Vanessa says, ALL RIGHT. AND LET'S TAKE
SOME BIG, DEEP BREATHS
BEFORE WE BEGIN,
CHASE.
(BOTH INHALING AND EXHALING)
Vanessa says, ONE MORE.
(INHALING AND EXHALING)
Vanessa continues, BREATHE OUT. AND SAY, "BYE
AND THANK YOU" TO EVERYBODY.
Chase waves and says, BYE.
Vanessa says, THANK YOU
FOR JOINING US, CHASE.
An animated sun rises.
Notes on a tabletop display beside Vanessa read, Probability, the likelihood of something happening.
Shown through a fraction and number line. Use probability to make decisions and predictions.
Vanessa says, SO, TODAY, WE'RE GOING TO
TALK ABOUT PROBABILITY,
THE LIKELIHOOD
OF AN EVENT OCCURRING.
HAVE YOU EVER WONDERED
WHAT THE WEATHER PERSON
IS TALKING ABOUT WHEN THEY SAY,
"THERE'S A 50% CHANCE
OF RAIN OR SNOW"?
OR IF YOU HAVE A VERY SMALL
CHANCE OF WINNING THE LOTTERY?
WHAT ARE THEY TALKING ABOUT?
TODAY, I'M GOING TO SHOW YOU
HOW YOU CAN SOLVE
FOR PROBABILITY
USING FRACTIONS
AND A NUMBER LINE.
WE'RE GOING TO USE PROBABILITY
TO MAKE DECISIONS
AND FUTURE PREDICTIONS.
SO, IF YOU HEARD THAT
THERE WAS A SNOWSTORM COMING,
YOU WOULD PRETTY--
YOU'D BE PRETTY WELL
TO BRING SNOW PANTS
AND MITTENS TO SCHOOL THAT DAY,
SO YOU'RE PREPARED FOR
THE WEATHER.
WE'RE GOING TO PLAY SOME
FUN GAMES TODAY WITH SPINNERS,
DICE AND CARDS.
SO, I WOULD LOVE FOR YOU
TO GET THOSE MATERIALS
IF YOU HAVE THEM LAYING AROUND,
OR YOU COULD MAKE
YOUR OWN CARDS.
YOU COULD MAKE YOUR OWN DICE.
I MADE THESE OUT OF
A PIECE OF CARDBOARD.
IT'S VERY SIMPLE. ALL YOU NEED
TO MAKE THE CARDBOARD DIE
ARE TAPE, CARDBOARD AND MARKERS.
IF YOU HAVE SOMETHING LIKE
A LAZY SUSAN LAYING AROUND--
YOUR PARENTS
WILL KNOW WHAT THAT IS--
YOU CAN TAPE SOME PAPER TO IT
AND IT'LL SPIN LIKE A SPINNER,
OKAY?
Vanessa holds up a lazy susan covered with colored paper in white, blue, red and yellow quadrants.
Vanessa says, I USED JUST YOUR RUN-OF-THE-MILL
DECK OF CARDS.
IF YOU HAVE A COIN OR TWO,
WE COULD DO SOME COIN TOSSES
LATER ON.
I'M GOING TO SHOW YOU SOME
REALLY COOL GAMES AND ACTIVITIES
YOU COULD DO WITH YOUR FRIENDS.
BUT BEFORE WE DO, LET'S WATCH
THIS EPISODE OF
LADY VOCAB,
WHO'S GOING TO GO INTO
THE DEFINITION OF PROBABILITY
USING A REALLY COOL SONG.
CHECK IT OUT, AND I'LL CATCH YOU
BACK HERE AFTER.
The animated sun rises.
A title screen reads, The Lady Vocab Show.
Professor P stands in a dark room in front of a monitor ‘with Lady Vocab’ written several times on it.
He wears a black sweater with a large letter P on the front. He has short dark hair and wears glasses.
Professor P says, HEY THERE, WORD FANS,
AND WELCOME TO
THE
LADY VOCAB SHOW.
I'M YOUR HOST,
PROFESSOR P.
AND NOW TO INTRODUCE
THE LONG-WINDED LADY HERSELF,
LADY VOCAB.
Lady Vocab stands behind a microphone.
She has shoulder length blonde hair and wears large sparkling silver glasses, and a black and white costume with the words window, shuttle, machine, and package written on it.
She says, THANKS, PROFESSOR.
ARE YOU READY
TO ROCK THE WORD?
Professor P says, YES, INDEEDY, MILADY.
THE WORD IS "PROBABILITY,"
WHICH IS A TERM THAT MEANS
HOW LIKELY SOMETHING
IS TO HAPPEN.
Lady Vocab says, HIT IT.
(Electronic music plays)
She sings, P-R-O-B-A-B-I-L-I-T-Y
Professor P says, PROBABILITY.
Lady Vocab sings, THE CHANCES THAT
YOU'RE LIKELY TO SUCCEED
JUST USE PROBABILITY
Professor P says, MM-HMM.
Lady Vocab sings, TOSS A COIN, IT'S 50-50
Professor P says, COULD BE HEADS
OR TAILS.
Lady Vocab sings, THE OUTCOME
IS FOR YOU TO SEE
Professor P says, THAT'S RIGHT.
Lady Vocab sings, PROBABILITY
SEEMS LIKELY
Professor P says, MM-HMM.
COULD BE.
Lady Vocab sings, PROBABILITY
CHANCES MAKE YOU LUCKY
Professor P says, HOW LIKELY?
Lady Vocab sings, PROBABILITY.
Professor P says, HMM. WELL, THERE YOU HAVE IT.
THE LIKELIHOOD THAT
I'LL SEE YOU NEXT TIME?
100%, WORD FANS. BYE FOR NOW.
Lady Vocab sings, PROBABILITY
YOU'RE SO LUCKY, PROBABILITY
A red logo over a black background reads, TVO kids. Copyright, The Ontario Educational Commissions Authority MMXIV
The animated sun rises.
Vanessa says, WELCOME BACK.
SO, TODAY WE'RE GOING TO TALK
ABOUT THEORETICAL PROBABILITY.
The caption reads, Junior 4-6. Teacher Vanessa.
A formula written on the tabletop display reads, theoretical probability equals number of favorable outcomes divided by number of possible outcomes.
Vanessa continues, WHAT DOES THAT MEAN?
WHAT ARE YOUR ODDS OF WINNING
WHEN YOU PLAY A GAME?
WHAT ARE YOUR ODDS
OF ROLLING ANY NUMBER ON A DICE?
Vanessa holds up a die.
She continues, WHAT ARE THE ODDS OF GETTING
A HEADS OR TAILS
WHEN YOU FLIP A COIN?
Vanessa holds up a coin.
She continues, AND IF YOU WANTED TO PLAY A GAME
WITH YOUR FRIENDS,
WHAT ARE THE ODDS OF PICKING UP
AN EIGHT IN CRAZY EIGHTS?
LET'S FIGURE THIS OUT.
SO, THEORETICAL PROBABILITY,
OR PROBABILITY,
IS KNOWN AS THE NUMBER
OF FAVOURABLE OUTCOMES
OVER, OR DIVIDED BY
IN A FRACTION FORM,
THE NUMBER OF POSSIBLE OUTCOMES.
SO, WHAT DOES THAT MEAN?
LET'S SAY I HAVE A DICE.
WE KNOW THAT THERE ARE SIX SIDES
TO A DICE,
AND EVERY SIDE HAS A NUMBER
RANGING FROM ONE TO SIX.
Vanessa rolls the die and says, SO, IF I WERE TO ROLL THIS DICE
AND I GET THE NUMBER SIX,
TECHNICALLY I HAVE
A ONE-OUT-OF-SIX PROBABILITY
OF GETTING ANY NUMBER
ON THIS DICE.
IN THIS CASE, I DID ROLL A SIX.
OKAY?
SO, LET'S SAY
I SAID TO MY FRIEND,
"IF I ROLL A FIVE,
I WIN THE GAME."
WHAT ARE MY ODDS OF WINNING?
I KNOW THAT I HAVE TO ROLL
JUST A FIVE,
SO THAT WOULD JUST BE A ONE,
LIKE WE HAVE HERE.
Vanessa holds up a blue card with the fraction 1/6 written on it.
She says, AND THERE ARE
SIX POSSIBLE OUTCOMES
'CAUSE THERE ARE SIX NUMBERS
ON A DICE.
SO, I HAVE A ONE-IN-SIX ODD
OF WINNING THE GAME.
LET'S SEE IF I DID WIN.
Vanessa rolls the die.
She says, NO. I ROLLED A FOUR.
SO UNFORTUNATELY,
MY FRIEND WON THAT ROUND.
FORTUNATELY FOR HER.
OKAY?
Vanessa removes the formula from the display, then picks up the lazy Susan spinner.
She says, LET'S TRY PLAYING WITH
OUR SPINNER.
AND WE HAVE
ONE, TWO, THREE, FOUR
DIFFERENT-COLOURED SECTIONS.
THAT MEANS THE SPINNER
CAN LAND ON
ANY ONE OF THE FOUR SECTIONS.
SO, MY POSSIBILITY--
PROBABILITY OF LANDING
ON THE WHITE, FOR EXAMPLE,
IS ONE OVER FOUR.
MY PROBABILITY OF LANDING
ON THE BLUE
IS ONE OUT OF THE TOTAL OF FOUR
DIFFERENT OPTIONS THERE ARE.
SO, YOU MIGHT SAY
TO YOUR FRIEND,
"IF I LAND ON RED, I WIN,
"BUT IF YOU LAND--
WHEN YOU SPIN AND YOU LAND
ON BLUE, YOU WIN."
SO, LET'S JUST SAY-- LET'S TRY.
I'M GOING TO SAY IF I LAND
ON RED, I GET ONE POINT.
Vanessa spins the spinner and says,
SO, I HAVE MY SPINNER.
I'M GOING TO TURN IT AROUND
AND UNFORTUNATELY,
I LANDED ON--
OH, WAIT, (UNCLEAR).
OH, NO. I LANDED ON THE WHITE.
SO, I DIDN'T GET A POINT, OKAY?
SO, LET'S SAY
IT'S MY FRIEND'S TURN.
AND THIS IS HARDER THAN IT SEEMS
TO HOLD.
(LAUGHING)
Vanessa spins the spinner and says,
AND IT LANDS ON BLUE,
BUT SHE NEEDED RED TO WIN.
SHE DOESN'T WIN.
SO, EITHER WAY, ONE OF US--
OR EACH OF US, I SHOULD SAY,
HAS A ONE-IN-FOUR CHANCE
OF WINNING THAT GAME.
IF I SAID I NEED TO LAND
ON RED
OR
BLUE TO WIN,
WHAT IS MY POSSIBILITY NOW,
MY PROBABILITY OF WINNING?
WE HAVE ONE-HALF.
WHY IS THAT ONE-HALF?
BECAUSE I COULD WIN ONE, TWO
OF A POSSIBLE
ONE, TWO, THREE, FOUR.
SO, TWO OUT OF FOUR
IS THE SAME AS
HAVING THE ODDS
OF HAVING ONE-HALF.
Vanessa holds up a blue card with the fraction 1/2 on it.
She says, SO, PLOTTING THIS
ON A NUMBER LINE,
I'M GOING TO SHOW YOU
SOME TERMS...
Vanessa picks up a long brown sheet of paper with a number line drawn on it.
Notes on the line from left to right read, impossible, unlikely, equally likely, likely, and certain.
The number 0 is at the left end. The number 1 is at the right.
Vanessa continues, ...THAT YOU ARE GOING TO BE
USING
IN MATHEMATICS FOR PROBABILITY.
I LOVE THE NUMBER LINE.
SO, IN THIS CASE
FOR PROBABILITY,
WE HAVE "UNLIKELY"
AND "IMPOSSIBLE"
STARTING AT THE ZERO.
SO, FOR EXAMPLE, YOUR ODDS
OF WINNING THE LOTTERY
ARE VERY, VERY UNLIKELY.
NOT IMPOSSIBLE,
'CAUSE "IMPOSSIBLE" MEANS
IT COULD NEVER HAPPEN.
BUT SOMEWHERE IN THE REALM OF
UNLIKELY TO IMPOSSIBLE.
SO, "IMPOSSIBLE" COULD BE
"THE SUN WON'T RISE TOMORROW,"
WHEN WE KNOW THAT CERTAINLY,
THE SUN WILL RISE EVERY DAY.
SO, WE'RE GOING TO MOVE
FROM IMPOSSIBLE TO UNLIKELY.
LIKE WE SAID,
WINNING THE LOTTERY,
LIKE WE SAID, SPINNING, UM,
MAYBE A WHEEL THAT HAD
A HUNDRED NUMBERS ON IT
AND YOU HAVE TO GET
ONE OF THE NUMBERS.
IT'S VERY UNLIKELY THAT
THE WHEEL WILL SPIN
ON YOUR NUMBER,
FROM ONE OUT OF A HUNDRED.
OKAY? AGAIN, NOT IMPOSSIBLE,
'CAUSE IT MIGHT HAPPEN.
BUT IT COULD BE UNLIKELY.
"EQUALLY LIKELY" MEANS
SOMETHING WILL HAPPEN
AS LIKELY AS IT WILL NOT HAPPEN.
SO, IF I PICK UP A COIN,
FOR EXAMPLE,
I KNOW THAT IT HAS A HEAD
AND A TAIL.
AND BECAUSE THERE'S
ONLY TWO OPTIONS, AGAIN,
I HAVE A ONE-OUT-OF-TWO ODD
OR PROBABILITY
THAT I WOULD ROLL-- OR, SORRY.
FLIP A COIN
AND LAND ON A HEAD.
I HAVE A ONE-IN-TWO PROBABILITY,
THEN,
THAT IT WOULD ALSO--
IT WOULD LAND ON A TAIL.
OKAY? SO, WHEN SOMETHING
IS EQUALLY LIKELY TO HAPPEN
AS IT'S
NOT LIKELY TO HAPPEN,
YOU HAVE A 50-50 CHANCE,
A ONE-OUT-OF-TWO SHOT,
IT IS EQUALLY LIKELY.
A yellow star is in the middle of the number line over the number 0.5.
Vanessa says, UM, SO, FOR SOMETHING TO BE
LIKELY TO HAPPEN,
WE CAN TALK ABOUT SOMETHING LIKE
IF THE WEATHER PERSON SAYS
THERE'S A 75% CHANCE
OF RAIN TODAY,
THAT IS LIKELY
THAT IT WILL HAPPEN.
HOW DO WE KNOW? WE KNEW THAT
SOMETHING CLOSER TO ONE
IS ABSOLUTELY CERTAIN TO HAPPEN.
SO, FOR EXAMPLE,
IF WE SAID YOU HAVE, UM--
IF YOU SPUN A WHEEL
AND IF YOU GOT ANY OF
THE THREE COLOURS EXCEPT WHITE,
YOU WIN, THAT IS LIKELY
THAT YOU WILL WIN THAT GAME,
BECAUSE YOU COULD LAND
ON YELLOW, RED, BLUE,
AND STILL WIN.
THE ONLY WAY YOU WOULD LOSE IS
IF YOU LANDED ON WHITE.
SO, THAT IS
A LIKELY PROBABILITY
THAT YOU WILL WIN.
SOMETHING CERTAIN IS THAT
YOU WILL TURN PLUS-ONE
ON YOUR NEXT BIRTHDAY.
SO, IF YOU ARE NINE, ON YOUR
NEXT BIRTHDAY YOU WILL TURN 10.
IF YOU'RE 10,
ON YOUR NEXT BIRTHDAY
YOU WILL CERTAINLY TURN 11.
YOU ARE AN AWESOME PERSON.
THAT IS CERTAIN.
SO, THAT'S 100% POSSIBILITY.
YOU'RE GREAT AT MATH?
100% POSSIBILITY. TRUST ME.
OKAY? SO, WE HAVE THE RANGE OF
SOMETHING IMPOSSIBLE HAPPENING,
OKAY?
SO AGAIN, WE SAID THAT
UNFORTUNATELY,
IF YOU THOUGHT THAT
THE SUN WILL NOT RISE TOMORROW,
IMPOSSIBLE.
YOU MIGHT WIN THE LOTTERY?
SOMEWHERE IN THE REALM
OF UNLIKELY AND IMPOSSIBLE.
SO, EVERY DAY, WHEN YOU BUY
YOUR LOTTERY TICKET,
AND YOU HAVE A 1 IN 33,000,000
CHANCE OF WINNING,
UNFORTUNATELY THE ODDS ARE
VERY, VERY LOW THAT YOU WIN,
BUT THEY'RE NOT IMPOSSIBLE.
SO, WE HAVE
"WINNING THE LOTTERY"
WOULD BE SOMEWHERE POSSIBLY
CLOSER TO THE ZERO HERE.
BUT DON'T GIVE UP HOPE, FRIENDS,
AS YOU GET OLDER.
(LAUGHING)
AGAIN, "EQUALLY LIKELY,"
WE'RE TALKING ABOUT
FLIPPING A COIN
AND THERE'S ONLY TWO OPTIONS.
(CLEARING THROAT)
WE'RE
TALKING ABOUT PLAYING CARDS,
WHEN YOU ONLY HAVE
RED OR BLACK SUITS.
Vanessa holds up two playing cards.
She continues, YOU'RE EQUALLY LIKELY
TO PICK UP A RED CARD
AS YOU ARE A BLACK CARD.
WE HAVE SOMETHING "LIKELY"
AS 75%,
OR THREE OVER FOUR.
WE TALKED ABOUT THE SPINNER.
WE SAID YOU WON--
WHEN THE GAME IS YOU CHOOSE
RED, YELLOW OR BLUE
OUT OF A TOTAL OF FOUR OPTIONS,
IT'S LIKELY THAT YOU WILL WIN.
AND THEN "CERTAIN," WE TALKED
ABOUT YOU GETTING A YEAR OLDER
FOR YOUR AGE NEXT YEAR, AND FOR
THE SUN SETTING THE NEXT DAY.
SO, WHEN YOU'RE WATCHING TV
AND MAYBE YOU'RE CATCHING
YOUR PARENTS WATCHING THE NEWS,
AND THE WEATHER PERSON SAYS,
"THERE'S A 10% CHANCE
OF PRECIPITATION TONIGHT,"
Vanessa holds a sheet of paper that reads, unlikely, 10%, 1/10, 0.1.
She continues, OKAY, THAT MEANS THAT
THERE'S A ONE-IN-10 CHANCE
OF IT RAINING TONIGHT.
THIS IS EQUIVALENT, MEANING
THAT IT'S THE SAME THING,
WHICH ALSO IS EQUIVALENT TO
ONE-TENTH OUT OF ONE,
FROM ZERO TO ONE.
SO, AGAIN, VERY, VERY UNLIKELY
THAT THIS WOULD HAPPEN.
OKAY? VERY UNLIKELY
FOR THERE TO BE RAIN TODAY.
Vanessa holds a sheet of paper that reads, equally likely, 50%, 5/10, 0.5.
She says, SIMILARLY,
IF SHE SAYS THERE'S A 50--
HE OR SHE SAYS THERE'S
A 50% CHANCE OF RAIN TODAY,
WE KNOW THAT
THAT'S EQUALLY LIKELY.
IT MIGHT RAIN
AS MUCH AS IT MIGHT NOT RAIN.
OKAY? SO, IN THIS CASE,
BETTER TO BE SAFE THAN SORRY.
I WOULD BRING AN UMBRELLA
OR A RAIN JACKET,
WHEREVER YOU'RE GOING.
Vanessa holds a sheet of paper that reads, certain, 90%, 9/10, 0.9.
Vanessa continues, AND IF SHE SAID--
OR HE SAID, I SHOULD SAY--
A 90% CHANCE OF RAIN TODAY,
IT'S ALMOST CERTAIN
THAT IT'S GOING TO RAIN.
SO, IN THIS CASE,
I WOULD USE THIS PROBABILITY
TO MAKE A DECISION
AND BRING AN UMBRELLA,
RAIN JACKET, RAIN BOOTS
TO SCHOOL
OR WHEREVER YOU'RE GOING TO PLAY
THAT DAY.
SO, YOU SEE
Vanessa holds up the number line and continues,
FROM OUR NUMBER LINE
THAT PROBABILITY RANGES
FROM ZERO, WHICH MEANS,
WHICH IS-- SORRY--
EXTREMELY UNLIKELY, IMPOSSIBLE.
TO ONE, WHICH IS MEANING
CERTAINLY SOMETHING WILL HAPPEN.
OKAY?
SO, IN THE NEXT SEGMENT,
WHEN WE TALK ABOUT
DIFFERENT GAMES,
WE'RE GOING TO PLOT THIS
AND DIFFERENT SCENARIOS
THAT YOU MIGHT DEAL WITH
ON A DAILY BASIS
ON OUR NUMBER LINE.
LET'S PLAY ONE MORE GAME
BEFORE WE WATCH OUR NEXT SHOW.
I HAVE A DECK OF CARDS HERE.
AND THEY RANGE FROM ACE
ALL THE WAY UP TO 10, AND
THEN WE HAVE THREE FACE CARDS
WITH THE ACE.
SORRY. THREE FACE CARDS.
SO, EACH SUIT HAS 13 CARDS.
WE HAVE THE HEARTS,
THE DIAMONDS, THE SPADES
AND THE CLUBS.
Vanessa shuffles a deck of cards and says,
IF I SAID TO YOU, "WHAT ARE
THE ODDS OF PICKING UP
A SUIT OF HEARTS
OUT OF MY DECK,"
WHAT WOULD THE ODDS BE?
Vanessa puts the formula back onto the display and says,
KNOWING THAT OUR
THEORETICAL PROBABILITY, AGAIN,
IS THE NUMBER
OF FAVOURABLE OUTCOMES--
SO, WE KNOW THAT THERE ARE
13 HEARTS IN OUR DECK.
OVER HOW MANY TOTAL
OR POSSIBLE OUTCOMES ARE THERE.
WE KNOW THAT THERE ARE 52 CARDS
IN THE DECK.
SO, 13 OVER 52
IS OUR FRACTION THAT WE USE,
Vanessa holds up a blue card with the fraction 13/52 on it.
She continues, WHICH IS THE SAME THING
AS ONE OVER FOUR.
SO, WE HAVE
A ONE-OUT-OF-FOUR CHANCE
OF PICKING UP A HEART WHEN I...
...QUICKLY SHUFFLE.
AND I'M GOING TO PICK
THE FIRST CARD ON TOP.
SO, I HAVE
A ONE-OUT-OF-FOUR CHANCE,
WHICH UNFORTUNATELY IS UNLIKELY.
OR MAYBE YOU DON'T WANT
TO PICK A HEART.
THAT'S YOUR FAVOURITE SUIT.
BUT LET'S SAY IT'S UNLIKELY
THAT YOU'RE GOING TO PICK
A HEART, A CARD THAT HAS
THE SUIT OF A HEART IN IT.
COMPARED TO--
THERE'S STILL CLUBS.
THERE'S STILL SPADES.
AND THERE'S STILL DIAMONDS.
SO, YOU'RE MORE LIKELY TO PICK
ONE OF THE OTHER THREE SUITS
THAT ARE REMAINING.
SO, ARE YOU READY TO SEE
IF I CAN PICK A HEART?
Vanessa draws the ace of hearts out of the deck of cards.
She says, OH, MY GOODNESS!
I DID.
(LAUGHING)
OKAY. SO, EVEN THOUGH MY ODDS
WERE UNLIKELY
THAT I WOULD PICK THIS,
ONE OUT OF FOUR,
I WAS STILL ABLE TO DO IT.
SO, THERE'S STILL HOPE OUT THERE
FOR ALL OUR LOTTERY PLAYERS.
ANYWAYS, I WOULD LIKE NOW
JUST TO THROW TO HAMZA,
AND HE IS FROM THE SHOW
LOOK KOOL,
AND HE'S GOING TO GO THROUGH
SOME AWESOME PROBABILITY GAMES,
EXPERIMENTS AND DEFINITIONS
OVER THE COURSE OF
A FEW MINUTES.
I HOPE YOU REALLY ENJOY,
AND I'LL SEE
ALL YOU PROBABILITY LOVERS
HERE AFTER THE VIDEO.
The animated sun rises.
Hamza flips a coin. He is clean shaven with short dark hair.
He wears a navy blue dress shirt and an orange and white striped bow tie.
Hamza says, OKAY.
HEADS.
TAILS? LET'S TRY IT AGAIN.
TAILS.
HEADS?
WHAT ARE THE ODDS I'M EVER
GOING TO GET THIS RIGHT?
TO FIND OUT,
WE'LL MEET A BIG CARD...
A man wearing Jack of Hearts costume enters the room.
(IN FRENCH ACCENT)
The man says, I AM JACQUES DESCARTES.
Hamza says, YEAH. YOU'RE THE ONE I NEEDED
TO WIN GO FISH YESTERDAY.
A clip plays.
...LAUNCH POWERFUL ROCKETS
YOU CAN BUILD AT HOME...
WHOA!
...AND DISCOVER AN UNBELIEVABLE
SCIENTIFIC FACT...
A young girl kneels and puts a microphone to a small white dog’s face.
She says, WHEN'S YOUR BIRTHDAY?
MINE IS NOVEMBER 9TH.
OH. WE HAVE A MATCH.
Hamza says, ...ON
LOOK KOOL.
(Upbeat music plays)
Hamza spins and puts on sunglasses. He wears a blue shirt and a white and blue striped bow tie.
Colorful geometric shapes fall onto a grassy field. The shapes grow to form a colorful city skyline.
(KOOL KATT MEOWING)
Colorful bridges form over a river. A yellow staircase rotates around a red tower.
A purple airplane circles the tower. Koolkatt watches an orange tower rise from the ground.
The title, Look Kool appears over a blue sky.
A coin shoots out of KoolKatt’s toaster-shaped back.
Hamza catches it and says, HEADS.
TAILS AGAIN.
HOW IS THIS POSSIBLE?
THAT'S, LIKE, 10 IN A ROW NOW.
KOOL CAT AND I
ARE PLAYING FLIP THE COIN.
AND SO FAR, HE'S WON EVERY TIME.
(LAUGHING)
MAYBE I NEED SOME OLD FASHIONED
LUCKY CHARMS,
LIKE THIS FOUR-LEAF CLOVER
AND THIS HORSESHOE.
OKAY, OKAY. ONE MORE.
ONE MORE. LET'S GO.
KoolKatt shoots out another coin.
Hamza catches it and says, HEADS.
TAILS AGAIN.
HOW IS THIS POSSIBLE?
THAT'S, LIKE, 10 IN A ROW NOW.
IT LOOKS LIKE
YOU COULD USE SOME HELP.
WHO ARE YOU?
Jacques enters the room.
He says, I AM JACQUES DESCARTES.
PERHAPS YOU REMEMBER ME
FROM YOUR DECK OF CARDS, NO?
Hamza says, YEAH. YOU'RE THE ONE I NEEDED
TO WIN GO FISH YESTERDAY.
NOW YOU DECIDE TO SHOW UP?
Jacques says, AND DO NOT BLAME ME
FOR PROBABILITY.
I DO NOT MAKE THE RULES.
Hamza says, PROBABILITY? WHAT'S THAT?
Jacques says, PROBABILITY IS A TYPE OF MATH
THAT HELPS PREDICT HOW LIKELY
SOMETHING IS TO HAPPEN.
Hamza says, WAIT. YOU MEAN MATH
CAN TELL ME HOW LIKELY IT IS
I'LL GET THE CARD I NEED
IN GO FISH,
OR WIN A COIN TOSS?
Jacques says, UH, YES.
I MEAN, WE CARDS KNOW ABOUT IT,
BUT WE PLAY
GAMES OF CHANCE ALL DAY LONG.
Hamza says, CAN YOU TELL ME
WHY KOOL CAT KEEPS WINNING?
Jacques says, I KNOW EXACTLY WHY KOOL CAT
KEEPS WINNING.
AND MAYBE YOU'LL FIGURE
THAT OUT FOR YOURSELF, EH?
(SNORTING ARROGANTLY)
KoolKatt shakes his head.
Hamza says, OKAY. CAN YOU TELL ME
HOW PROBABILITY WORKS?
Jacques says, OF COURSE.
PROBABILITY IS
THE NUMBER OF OUTCOMES YOU WANT
DIVIDED BY THE NUMBER
OF POSSIBLE OUTCOMES.
Hamza says, OH, OKAY.
SO, I WANT HEADS, AND THERE'S
ONLY TWO POSSIBLE OUTCOMES,
HEADS OR TAILS.
SO, THAT'S ONE DIVIDED BY TWO,
WHICH IS THE SAME AS ONE-HALF.
SO, TECHNICALLY, IT SHOULD BE
ON HEADS HALF THE TIME, RIGHT?
Jacques says, YOU'RE RIGHT.
IT SHOULD.
BUT EVEN WITH MY LUCKY
FOUR-LEAF CLOVER AND HORSESHOE,
KOOL CAT KEEPS WINNING.
Jacques snorts and says, LUCK HAS NOTHING TO DO WITH IT.
An animated 4-leaf clover walks through a field of clovers and says, OH, BOY. I FEEL LUCKY TODAY.
A brown shoe steps on the clover. The clover sticks to the bottom of the shoe, then frees itself.
The clover says, OOH. I SHOULD HAVE BROUGHT
MY LUCKY HORSESHOE.
A horseshoe falls on the clover.
The clover says, OH, MAN.
Hamza says, CAN YOU USE PROBABILITY
TO PREDICT
ANYTHING
OTHER THAN GAMES?
Jacques says, UH, YES, ABSOLUTELY.
I MEAN, PROBABILITY CAN TELL YOU
HOW LIKELY IT IS
THAT YOU'LL FIND A PEARL
IN AN OYSTER.
An animated oyster opens. A pearl is inside it.
Jacques continues, ONE IN 12,000.
OR HOW LIKELY IT IS THAT
A FAMILY WILL HAVE TRIPLETS.
ONE IN 44,000.
A picture of triplets appears.
Jacques continues, OR IT CAN TELL YOU
HOW LIKELY IT IS
THAT A GROWN-UP PERSON
WILL GO TO THE EMERGENCY ROOM
WITH A POGO STICK INJURY.
ONE IN 115,300.
A man hops on a pogo stick, then crashes.
The man says, OW!
Hamza says, SO, PROBABILITY IS AN
EXACT WAY TO LOOK AT THINGS?
Jacques says, UH, IT'S NOT EXACT.
BUT IT DOES SHOW YOU
HOW LIKELY OR UNLIKELY
IT IS TO HAPPEN.
Hamza says, OH, YEAH.
I MEAN, IF SOMETHING'S UNLIKELY,
THAT DOESN'T MEAN
THAT IT'S IMPOSSIBLE.
I MEAN, UNLIKELY THINGS
HAPPEN ALL THE TIME.
(Upbeat woodwind and tuba music plays)
Hamza flies through the sky wearing a pig costume. He flies in formation with several animated pigs.
He sings, NOT UNTIL PIGS FLY
THAT'S WHAT THEY SAY
WHEN SOMETHING'S UNLIKELY
BUT I'M HERE TODAY
FLAPPING MY WINGS
ON THE WAY TO THE SUN
THE ODDS WERE
200 TRILLION BILLION TO ONE
BUT JUST 'CAUSE IT'S RARE
DOESN'T MEAN IT'S NOT DONE
I SAID JUST 'CAUSE IT'S RARE
DOESN'T MEAN IT'S NOT DONE
OINK-OINK-OINK, OINK-OINK-OINK
OINK-OINK-OINK
SOMETIMES A RIVER
IS BACKWARDS FLOWING
SOMETIMES
A TURTLE IS NOT SO SLOWING
SOMETIMES IN SUMMER
IT STARTS SNOWING
AND NOW THAT
YOU'RE ALL KNOWING
I REALLY MUST BE GOING
OINK-OINK-OINK, OINK-OINK-OINK
OINK-OINK-OINK
Hamza says, SO, DO YOU THINK
KOOL KATT WINNING
10 TIMES IN A ROW
IS JUST PURE LUCK?
Jacques says, HA! I THINK
THAT'S AWFULLY IMPROBABLE.
Hamza says, YEAH. ME, TOO.
SO, WHAT ELSE CAN YOU TELL ME
ABOUT PROBABILITY?
Jacques says, OH, HERE IS ONE OF
MY FAVOURITE THINGS.
A graphic appears showing 23 human figures.
Jacques continues, IF YOU HAVE A ROOM OF 23 PEOPLE,
THERE IS A ONE IN TWO CHANCE
THAT TWO OF THEM
WILL HAVE THE SAME BIRTHDAY.
A box appears around two figures.
Hamza says, NOW, THAT DOESN'T
SOUND RIGHT.
I MEAN, THERE'S 23 PEOPLE
AND 365 DAYS IN A YEAR.
Jacques says, I DEAL IN PROBABILITY.
I KNOW WHAT I AM TALKING ABOUT.
Hamza says, OKAY, OKAY.
NO OFFENCE, MONSIEUR.
BUT I THINK I'M GOING TO
HAVE THE INVESTIGATORS
CHECK THIS OUT.
Jacques says, WELL, SUIT YOURSELF.
An animated KoolKatt looks through a magnifying glass.
An announcer says, INVESTIGATION.
A young boy and girl appear on a screen.
Hamza says, HI, INVESTIGATORS.
The kids say, HI, HAMZA.
Hamza says, ALEXANDRA, ETHAN,
I HAVE A QUESTION FOR YOU.
A TYPICAL YEAR
HAS 365 DAYS, RIGHT?
Alexandra and Ethan say, YEAH.
RIGHT.
Hamza says, SO, HOW MANY DIFFERENT
BIRTHDAY DATES
COULD THERE BE IN THE YEAR?
Alexandra and Ethan say, 365?
Hamza says, EXACTLY. SO, HOW MANY
PEOPLE DO YOU THINK
YOU'D HAVE TO ASK
BEFORE YOU'D FIND TWO
WITH THE SAME BIRTHDAY?
Alexandra says, WELL, I THINK WE SHOULD
DIVIDE IT IN TWO,
'CAUSE WE NEED
TWO PERSONS.
Ethan says, OR 185?
Alexandra says, YEAH, ABOUT THAT.
Hamza says, YOU KNOW, I THINK IT
WOULD TAKE A LOT OF PEOPLE, TOO.
BUT I HAVE A BUDDY HERE WHO
THINKS YOU'D NEED A LOT LESS.
LET'S TEST IT.
ASK PEOPLE THEIR BIRTHDAYS
UNTIL YOU FIND A MATCH.
Ethan says, WE'RE ON IT.
The kids approach a group of people outside a large grey brick and stone building.
Ethan says, WE'RE DOING A TV SHOW
ON PROBABILITY,
AND WE'RE WONDERING
WHAT YOUR BIRTHDAY IS.
A woman says, THE 14TH OF FEBRUARY.
Alexandra asks, AND WHAT'S
YOUR BIRTHDAY?
A woman says, MARCH 24TH.
Alexandra kneels beside the small white dog and holds a microphone to its face. She asks, WHEN'S YOUR BIRTHDAY?
COME ON, TELL ME.
The dog’s male owner says, HE ONLY
SPEAKS FRENCH.
Alexandra says, OH.
A line graph appears.
A computerized voice says,
ACCORDING TO THE LAWS
OF PROBABILITY,
IN A ROOM WITH 23 PEOPLE,
IT'S MORE THAN 50% CERTAIN
THAT AT LEAST TWO
WILL HAVE THE SAME BIRTHDAY.
WITH 30 PEOPLE IT'S 75%,
AND WITH 70 IT'S 99%.
BY DOING LOTS OF EXPERIMENTS
LIKE THESE,
WE CAN SEE THAT THE LAWS
OF PROBABILITY WORK.
Ethan holds a microphone up to a woman and asks, AND YOU?
The woman says, MAY THE 18TH.
Several women answer Alexandra and Ethan, MAY 26TH.
SEPTEMBER 6TH.
FEBRUARY 22ND.
AUGUST 28TH.
MAY THE 18TH.
Ethan says, WE GOT TWO.
Hamza says, WOW!
Alexandra says, ALL RIGHT.
THANK YOU.
Hamza asks, HOW MANY DID IT TAKE?
Alexandra counts checkmarks on a grid and counts, ONE, TWO, THREE,
FOUR, FIVE, SIX,
SEVEN, EIGHT, NINE,
10, 11, 12, 13.
Ethan says, JUST 13.
Alexandra says, YEAH. A LOT LESS
THAN WE THOUGHT.
Hamza says, THAT'S A LOT LESS
THAN WE BOTH THOUGHT.
WE'LL CATCH UP
WITH THE INVESTIGATORS LATER.
BUT THE PROBABILITY THAT
I'M BLOWN AWAY BY THIS IS 100%.
Jacques says, AHA!
I KNEW HE'D SEE IT MY WAY.
Hamza continues, PROBABILITY SAYS THAT
A COIN SHOULD LAND HEADS
HALF THE TIME, RIGHT?
SO, MAYBE
I'LL JUST STICK TO HEADS,
AND MAYBE KOOL CAT'S COIN
WILL LAND ON HEADS
A BUNCH OF TIMES IN A ROW.
Koolkatt shakes his head.
Jacques says, AH, EXCUSEZ-MOI.
HOLD YOUR HORSES.
UH, YOU'VE FALLEN FOR
THE MONTE CARLO FALLACY.
Jacques plays Go Fish with KoolKatt.
Jacques says, UH--
GO FISH.
Hamza says, THE MONTE CARLO
WHAT-ACY?
Jacques says, FALLACY. IT'S WHEN
SOMETHING IS NOT TRUE.
IN THIS PARTICULAR CASE,
IT IS THE IDEA THAT
IF YOU'VE HAD BAD LUCK,
YOUR LUCK
HAS TO CHANGE.
THE PROBABILITY OF FLIPPING
A COIN TO TAILS 10 TIMES IS--
IT'S SMALL.
BUT THE PROBABILITY
OF EACH INDIVIDUAL FLIP
IS THE EXACT SAME
EVERY TIME YOU FLIP IT.
DO YOU HAVE ANY THREES?
Koolkatt shakes his head.
Hamza says, I GUESS I STILL HAVE A LOT MORE
TO LEARN ABOUT PROBABILITY.
(Upbeat music plays)
Panels of a puzzle shift and become a picture of Koolkat.
A graphic of a cat head with ears inside it appears.
An announcer says, BRAIN BENDER
Hamza says, TODAY'S PUZZLE-SOLVERS
ARE EVAN AND ALYSSA.
HELLO.
Evan and Alyssa wave and say HI, HAMZA.
HI.
Hamza says, OUR BRAIN-BENDER
IS GOING TO BE A BIT DICEY.
YOU SEE A PAIR OF DICE,
RIGHT?
The kids say, YEAH.
Hamza says, THERE ARE 12 CUPS.
EACH CUP REPRESENTS A NUMBER YOU
COULD ROLL WITH A PAIR OF DICE.
HERE'S THE BRAIN-BENDER.
IF YOU ROLL A PAIR OF DICE
A LOT OF TIMES,
WHICH OF THESE 12 NUMBERS
DO YOU THINK
YOU'LL GET MOST OFTEN?
Evan says, FIVE. FOUR, MAYBE.
Hamza says, WELL,
LET'S FIND OUT.
Evan rolls the dice and says, FOUR.
He drops a token into a red and white cup labelled with the number 4.
Alyssa rolls the dice and says, SIX.
She drops a token into a cup labelled with the number 6.
Evan rolls the dice and says, SEVEN. THERE.
Alyssa rolls the dice and says, 10.
She rolls again and says, SEVEN.
SIX AND SEVENS
ARE IN THE LEAD.
The kids roll the dice repeatedly.
Hamza says, IT LOOKS LIKE THEY'RE ON A ROLL.
WE'LL CHECK BACK WITH THEM
LATER.
(BRAKES SQUEALING)
An animation shows blue and yellow KoolKatts racing down a street.
The announcer says, CHALLENGE.
Hamza stands in a park with two teams of one boy and one girl wearing yellow or blue shirts.
He says, WELCOME TO THE
LOOK KOOL
PROBABILITY CARNIVAL.
AND TO MY RIGHT, I HAVE KIKI
AND ZACHARY. TEAM YELLOW.
Kiki and Zacahry say, TEAM YELLOW.
Hamza continues, AND ON MY LEFT, I HAVE
ELENI AND DONATO. TEAM BLUE.
Eleni adn Donato says, TEAM BLUE.
Hamza and the kids approach a game with several picture of KoolKatt wearing a clown hat and nose.
Hamza says, FIRST UP, WE HAVE
THE BALL TOSS.
BUT BE WARNED.
ONE OF THESE CLOWNS
IS THE DREADED CLOWN OF DOOM.
A red mannequin head wears a colorful clown wig.
(EVERYONE GASPING)
Hamza says, MM-HMM. WHOEVER KNOCKS IT OVER
WILL FACE DIRE CONSEQUENCES.
ZACHARY, YOU GET TO GO FIRST.
He throws a ball through one of the KoolKatt pictures. Text over the clown head reads, safe.
Hamza says, OOH. LET'S TAKE A CLOSER LOOK AT
THIS WITH MY MIND'S EYEGLASSES.
Hamza puts on glasses.
A computerized voice says,
NOW THAT ONE OF
THE EIGHT CLOWNS
HAS BEEN ELIMINATED,
THE PROBABILITY OF HITTING
THE CLOWN OF DOOM
BECOMES ONE IN SEVEN.
Hamza removes the glasses and says, WHOA!
NOW IT'S TEAM BLUE'S TURN.
Kids take turns throwing balls at the wall of KoolKatt pictures.
Hamza says, YES.
WOO-HOO-HOO!
The computerized voice says, WITH EVERY SAFE SHOT,
THE DANGER INCREASES.
THE PROBABILITY
IS NOW ONE IN FIVE.
ALL RIGHT, DONATO.
Kids take turns throwing balls at the wall of KoolKatt pictures.
Hamza says, OOH.
KEANA, THE PROBABILITY IS?
Keana says, ONE OUT OF TWO.
Hamza says, ONE OF THESE IS
THE CLOWN OF DOOM.
LET'S FIND OUT WHICH ONE IT IS.
Keana throws a ball and knocks over a picture.
Hamza says, WOO-HOO-HOO!
DONATO, WHAT DO YOU THINK
IS THE PROBABILITY THAT
THAT IS THE CLOWN OF DOOM?
Donato says, ONE OUT OF ONE.
Hamza says, I'M PRETTY SURE
YOU'RE RIGHT.
Donato throws a ball at the last picture. It flips over revealing a picture of a clown.
(SIREN WAILING)
Hamza says, OH! THERE IT IS.
Donato says, UH-UH.
Water sprays Donato from the mouth of the red mannequin head.
He falls over laughing and says, UGH!
Hamza says, WELL, I THINK THE
PROBABILITY OF THIS CHALLENGE
GETTING WETTER IS REALLY HIGH
WHEN WE GET BACK.
Two red water balloons pop.
(EVERYONE CHEERING)
Hamza flips a coin and says, OH, HEADS. IF IT'S HEADS HALF
THE TIME I FLIP THE COIN,
HOW COME KOOL CAT KEEPS WINNING?
OH, WELL. LET'S SEE HOW
THE BRAIN-BENDER IS GOING.
Hamza approaches the screen and waves his hand.
Evan says, THE LAST ROLL
OF THE GAME IS...
Evan rolls the dice.
Evan and Alyssa say, ...FIVE.
Evan drops a token into a cup
He says, OH.
Hamza says, OKAY. IT'S TIME TO COUNT UP
HOW MANY TOKENS ARE IN EACH CUP.
Evan and Alyssa take tokens out of the cups and count,
12, WE HAVE FOUR.
SIX, 10.
THREE, SEVEN AND EIGHT.
WOW. WE GOT A LOT.
15.
IN SIX WE HAVE 13.
IN FIVE WE HAVE SEVEN.
FOUR, FIVE. SIX.
IN TWO, WE ONLY HAVE ONE.
AND IN ONE, NOTHING.
Evan says, YOU KNOW, IT'S ACTUALLY
IMPOSSIBLE TO GET A ONE,
BECAUSE THERE'S TWO DICE.
Hamza says, SO, TELL ME WHICH ONE
ACTUALLY HAD THE MOST.
The kids say, SEVEN.
Hamza says, DO YOU KNOW WHY?
Evan says, NO.
Hamza says, WHY DO YOU THINK
THEY CALL IT
LUCKY NUMBER SEVEN?
Evan says, MAYBE BECAUSE SEVEN ALWAYS WINS.
Alyssa says, A REALLY GOOD ANSWER,
I THINK.
Hamza says, PROBABLY.
THANKS, EVAN. THANKS, ALYSSA.
Evan and Alyssa wave and say, BYE, HAMZA.
BYE.
Evan rolls two yellow and orange dice and says,
THERE YOU GO. SEVEN.
I'M GOING TO SEE IF THERE'S
A MATHEMATICAL EXPLANATION
BEHIND "LUCKY SEVEN."
IF I HAVE TWO DICE,
HOW MANY DIFFERENT WAYS
CAN I ROLL SEVEN?
The animation of KoolKatt breaks into multiple pieces then reforms whole.
The announcer says, DECONSTRUCT.
Hamza says, DECONSTRUCT.
WHOA.
The dice float in mid air, rotating into various combinations of seven.
Hamza says, ARE YOU SEEING WHAT I'M SEEING?
THERE ARE A LOT OF POSSIBLE
COMBINATIONS TO MAKE SEVEN.
A graphic appears showing all possible dice combinations.
Hamza says, OH, AND LOOK.
THERE'S A PATTERN
TO THE COMBINATIONS.
THERE'S ONE WAY TO MAKE TWO,
TWO WAYS TO MAKE THREE,
THREE WAYS TO MAKE FOUR,
FOUR WAYS TO MAKE FIVE,
FIVE WAYS TO MAKE SIX,
AND SIX WAYS TO MAKE SEVEN.
THE NUMBER OF POSSIBILITIES
INCREASES BY ONE
UNTIL YOU GET
TO SEVEN.
AND THEN IT DECREASES
FOR EVERY NUMBER AFTER THAT
UNTIL YOU GET TO 12.
HEY, IT MAKES A TRIANGLE.
SO, "LUCKY SEVEN"
IS ACTUALLY JUST
THE MOST LIKELY NUMBER
THAT YOU CAN ROLL WITH TWO DICE.
IT'S NOT REALLY LUCK AT ALL.
The 4-leaf clover walks and smiles.
He says, OH, BOY. I FEEL LUCKY TODAY.
UH-OH.
(THUNDER CRASHING)
Rain falls on the clover, then lightning strikes it.
The clover lies on the ground and says, WELL, I GUESS I SHOULDN'T HAVE
CARRIED THIS BIG HUNK OF METAL
IN A THUNDERSTORM.
OH, NO.
Lightning strikes the horseshoe. The horseshoe falls on the clover.
The clover says, OH, MAN.
The animated KoolKatt looks through the magnifying glass.
The announcer says, INVESTIGATION.
A woman says, MY BIRTHDAY IS NOVEMBER 21ST.
Ethan and Alexandra chase after a pigeon.
They yell, WHEN'S YOUR BIRTHDAY?
NO, DON'T GO. WAIT!
A man says, NOVEMBER 16TH.
Ethan says, AND YOU?
Several people respond, NOVEMBER 9TH.
10TH OF MARCH.
22ND OF NOVEMBER.
MINE IS NOVEMBER 9TH.
Alexandra says, OH, WE HAVE A MATCH.
Hamza says, OKAY.
HOW MANY PEOPLE DID IT TAKE
TO GET A BIRTHDAY MATCH
THIS TIME?
Alexandra says, 37.
THAT'S NOT A LOT...
Ethan says, ...COMPARED TO
WHAT WE THOUGHT.
Alexandra says, YEAH. 180 COMPARED TO 37?
THAT'S NOTHING.
Hamza says, NEITHER TRY TOOK 180 PEOPLE.
Ethan and Alexandra say,
NO.
NOT EVEN CLOSE.
The line graph appears.
The computerized voice says, THE PROBABILITY
OF FINDING A MATCH
AFTER ASKING 13 PEOPLE
IS ONLY 19%.
THAT IS SOMEWHAT UNLIKELY.
THE PROBABILITY
OF FINDING A MATCH
AFTER 37 PEOPLE IS 85%.
VERY LIKELY.
AFTER ASKING ONLY 60 PEOPLE,
YOU ARE ALMOST CERTAIN
TO HAVE A MATCH.
Hamza says, THE NUMBER OF PEOPLE
IS A LOT LOWER
THAN WE THOUGHT.
READY TO DO
SOME ROCKET SCIENCE NOW?
Ethan says, YEAH.
Alexandra says, OH, YEAH. BIG TIME.
The animated sun rises.
Vanessa says, WELCOME BACK.
I HOPE YOU ENJOYED THE VIDEO.
The caption reads, Junior 4-6. Teacher Vanessa.
She continues, WE'RE GOING TO TALK ABOUT
THE ODDS
OF MULTIPLE EVENTS HAPPENING.
SO, YOU SEE TO MY RIGHT HERE,
OR YOUR LEFT,
THREE DIFFERENT SPINNERS.
AND WE HAD JUST TALKED ABOUT
THEORETICAL PROBABILITY
BEING THE NUMBER OF
LIKELY EVENTS
OVER THE TOTAL POSSIBILITY
OF EVENTS THAT COULD HAPPEN.
SO, IF WE LOOK FIRST
ON THIS SPINNER,
IF I WANTED TO LAND ON
ONE OF THE SIDES OF THE SPINNER,
I'D HAVE A PROBABILITY
OF ONE OVER TWO.
OKAY? SO, I COULD EITHER LAND
HERE OR I COULD LAND HERE.
Vanessa points at a circle divided into two sections.
She continues, THAT MEANS I HAVE
AN EQUALLY LIKELY PROBABILITY
THAT I'D LAND ON THE BLUE SIDE
Vanessa colors half the circle blue.
COMPARED TO LANDING ON
THE WHITE SIDE.
EQUALLY LIKELY.
IN THE MIDDLE SPINNER, I HAVE
ONE, TWO, THREE, FOUR SECTIONS.
SO, THE ODDS OF ME LANDING ON
ANY ONE OF THOSE FOUR SECTIONS
IS ONE OUT OF FOUR.
AND ON THE SPINNER HERE,
WE SEE THAT WE HAVE
ONE, TWO, THREE, FOUR,
FIVE, SIX.
SO, THE LIKELIHOOD OF ME LANDING
ON ANY ONE OF THOSE SECTIONS
OF THE SPINNER IS ONE OVER SIX.
OKAY? SO, AS YOU SEE,
YOUR ODDS OF LANDING ON
ANY ONE SECTION
GET SMALLER, EVEN THOUGH
THE FRACTION GETS BIGGER.
THE PERCENT GETS SMALLER
AS YOU HAVE MORE SECTIONS ADDED.
Vanessa removes the drawings of circular spinners from the tabletop display.
A new sheet reads, Red twice in a row: 1/4 x 1/4.
Vanessa continues, SO, WHAT HAPPENS IF ONE OF
YOUR FRIENDS AND YOURSELF
PLAY A GAME,
AND YOU ARE SPINNING
A WHEEL,
AND YOU HAVE FOUR SECTIONS.
AND THE WAY TO WIN IS IF
YOU LAND ON RED TWICE IN A ROW.
WHAT ARE YOUR ODDS
OF WINNING THE GAME?
OKAY?
SO, WE KNOW THAT WE HAVE
A ONE-OUT-OF-FOUR PROBABILITY
OF WINNING,
BECAUSE WE KNOW WE HAVE ONE RED
OUT OF A TOTAL OF FOUR.
OKAY? SO, AFTER ONE SPIN,
THAT'S THE PROBABILITY.
WHAT ARE THE ODDS
THAT YOU CAN GET IT TWICE?
SO, ON YOUR SECOND SPIN,
YOU AGAIN HAVE
A ONE-OUT-OF-FOUR PROBABILITY
OF YOU SPINNING A RED.
IN TOTAL,
TO FIND OUT WHAT OUR PROBABILITY
WOULD BE
FOR THESE TWO EVENTS HAPPENING
AFTER EACH OTHER,
WE CAN MULTIPLY
THE TWO FRACTIONS TOGETHER.
SO, WHEN WE MULTIPLY FRACTIONS,
WE LOOK TO MULTIPLY
THE NUMERATORS.
ONE TIMES ONE IS ONE.
AND WE PUT IT OVER
THE DENOMINATOR.
SO, WE MULTIPLY THOSE TWO
TOGETHER.
FOUR TIMES FOUR IS 16.
Vanessa writes the fraction 1/16.
She says, SO, MY ODDS OF ROLLING RED
TWICE IN A ROW
ON THIS WHEEL
ARE ONE OUT OF 16.
NOW, IF I'M PUTTING THAT ON
MY NUMBER LINE,
I KNOW THAT IT WOULD BE
ALMOST BETWEEN
IMPOSSIBLE AND UNLIKELY.
OKAY?
Vanessa points at the number line.
She says, SO, THIS IS A HARD GAME TO WIN,
TO GET TO ROLL--
OR TO SPIN RED TWICE IN A ROW.
BUT LET ME TRY, 'CAUSE I THINK
I WAS LUCKY ON THAT OTHER.
(LAUGHING)
THAT OTHER GAME.
I WAS PICKING A HEART. OKAY.
Vanessa spins the 4-colored lazy Susan wheel.
SO, UNFORTUNATELY, NO.
I ROLLED WHITE.
AND I ROLLED WHITE AGAIN.
SO, I WOULD NOT HAVE WON
ON MY GAME.
THE ODDS OF ME LOSING, THEN,
WOULD BE--
SO, THIS IS FOR A WIN.
AND THEN WE KNOW THAT
MY ODDS OF LOSING
WOULD BE 15 OUT OF 16.
SO, MUCH HIGHER
THAT I WOULD'VE LOST.
BECAUSE WE KNOW 15 OVER 16
PLUS ONE OVER 16
GIVES ME 16 OVER 16, OR A WHOLE.
OKAY? SO, UNFORTUNATELY,
I DIDN'T WIN THAT GAME.
Vanessa reveals a new sheet of paper on the display that reads, 3 heads in a row: 1/2 x 1/2 x 1/2
Vanessa continues, NOW, WHAT IF SOMEONE SAYS,
"CAN YOU FLIP A COIN
"SO THAT YOU GET HEADS
THREE TIMES IN A ROW?"
WELL, WHAT'S THAT PROBABILITY?
SO, ON THE FIRST ROLL,
I HAVE A ONE-IN-TWO SHOT,
BECAUSE WE TALKED ABOUT
HEADS OR TAILS
BEING THE TWO POSSIBILITIES,
AND WE SAID WE WANTED HEADS,
OKAY?
SO, THAT WOULD BE MY FIRST ROLL,
MY FIRST FLIP.
MY SECOND FLIP,
I HAVE THE SAME PROBABILITY.
AND MY THIRD FLIP, I HAVE TO GET
A ONE-OUT-OF-TWO SHOT
OF GETTING A HEAD.
WHAT IS THAT ALTOGETHER?
SO, WE CAN MULTIPLY
OUR FRACTIONS.
ONE TIMES ONE TIMES ONE,
YOU GET ONE.
OVER-- NOW, WE MULTIPLY
OUR DENOMINATORS TOGETHER.
TWO TIMES TWO IS FOUR.
TIMES TWO AGAIN IS EIGHT.
Vanessa writes the fraction 1/8.
She says, SO, I HAVE A ONE-OUT-OF-EIGHT
PROBABILITY
OF FLIPPING A COIN AND
RECEIVING HEADS, THREE IN A ROW.
THREE TIMES IN A ROW.
AGAIN, WE'RE LOOKING AT
THE "UNLIKELY" RANGE.
UM, SOMEWHERE IN BETWEEN HERE.
OKAY? SO, YOUR FRIEND
IS MORE LIKELY TO WIN
IF THEY SAID THAT
THEY COULD ROLL ANYTHING
BUT THREE HEADS IN A ROW.
IF THEY SAID THAT THEY COULD
ROLL EITHER A HEADS OR TAILS?
(LAUGHING)
AH, THAT WOULD BE SMART.
OKAY. SO, LET'S SEE IF I CAN
ROLL THREE HEADS IN A ROW.
Vanessa flips a coin and says,
ONCE, AND I PROMISE
I'M NOT CHEATING.
CAN YOU SEE THE REFLECTION?
OKAY.
She flips the coin again and says, NO. I GOT A TAIL.
OKAY? SO, I DIDN'T WIN AGAIN.
AND HOW DO WE KNOW THAT
IT WAS GOING TO BE DIFFICULT
FOR ME TO WIN THIS GAME?
BECAUSE WHEN WE PLOT IT
ON OUR NUMBER LINE,
WE SEE THAT ONE OUT OF EIGHT
IS A VERY SMALL FRACTION,
LESS THAN UNLIKELY.
SO, THAT GAME WOULD BE
VERY, VERY DIFFICULT TO WIN.
LET'S PLAY ONE MORE BEFORE
WE WATCH OUR NEXT EPISODE
OF
MATHXPLOSION.
Vanessa picks up a deck of cards and places a blue card with the fraction 26/52 on the display.
Vanessa says, UM, LET'S SEE IF I CAN
GET THESE ODDS HERE.
SO, WHAT DO YOU THINK
I'M GOING TO--
HOW CAN I WIN THIS GAME?
LET'S SAY I CAN PICK EITHER
TWO OF TWO DIFFERENT SUITS,
OR I COULD PICK, UM,
ONE RED CARD.
OKAY? SO, I KNOW THAT THERE ARE
26 RED CARDS IN THIS DECK.
AND THERE'S 26 BLACK CARDS
IN THIS DECK,
SO IT'S EQUALLY LIKELY THAT
I WOULD PICK A RED OR A BLACK.
SO, MY CHANCES ARE RIGHT IN
THE MIDDLE OF THAT NUMBER LINE,
THAT 0.5, OR ONE OVER TWO.
UM, LET'S GO THIS WAY.
ACTUALLY, NO. LET'S TRY IT.
LET'S DO IT THIS WAY AGAIN.
OKAY. SO, LET'S SEE MY ODDS OF
PICKING A BLACK CARD
ON THE TOP OF MY PILE.
Vanessa picks the 8 of hearts out of the deck.
Vanessa says, AND IT WAS A RED.
SO, UNFORTUNATELY, I DID NOT WIN
THE GAME
THAT I WOULD HAVE WON
IF I HAD DRAWN A BLACK CARD.
SO, I WAS EQUALLY LIKELY
TO WIN AND LOSE,
AND UNFORTUNATELY,
I TAKE THE LOSS ON THIS ONE.
SO, I WOULD LOVE FOR YOU TO
WATCH THIS NEXT EPISODE
OF
MATHXPLOSION.
IT'S GOING TO TEACH YOU
HOW SOCKS AND MATH TOGETHER
ARE AN AWESOME, AWESOME
MAGIC TRICK.
SO, CHECK IT OUT, AND I'LL
MEET YOU HERE AFTER THE VIDEO.
The animated sun rises.
(laser sounds)
Kids sing, WHAT A HIT
IT'S NOT A TRICK
IT'S
MATHXPLOSION
The MathXplosion logo appears.
The kids sing, JUST FOR YOU, COOL AND NEW
MATHXPLOSION
A brown-haired man with a neatly trimmed beard, carries a brown wooden drawer full of colorful socks.
He wears a red t-shirt with the MathXplosion logo on it.
The man says, DID YOU KNOW THAT I CAN FIND
TWO SOCKS OF THE SAME COLOUR
IN THIS MESSY SOCK DRAWER
WITH MY EYES CLOSED?
YEP, THAT'S RIGHT.
AND AS AMAZING
AS THAT SOUNDS ALREADY,
I NEED TO PICK
JUST FOUR SOCKS TO DO IT.
I'LL SHOW YOU HOW IT'S DONE.
YOU WON'T BELIEVE YOUR EYES.
The man opens the drawer. It is empty.
The man says, NEED SOME SOCKS, PLEASE.
GET SOME SOCKS.
The man stands behind a table.
I HAVE BEFORE ME
A DRAWER FULL OF SOCKS.
THESE SOCKS COME IN
THREE DIFFERENT COLOURS.
WE HAVE BLUE, GREEN AND PINK.
THE TOTAL NUMBER OF SOCKS
IN THE DRAWER
DOESN'T MATTER AT ALL,
AS LONG AS I KNOW
HOW MANY COLOURS THERE ARE.
IN THIS CASE, THREE COLOURS.
SO, WHAT I'M GOING TO DO IS
PULL JUST FOUR SOCKS
FROM THE DRAWER IN THE DARK.
AND I CAN GUARANTEE
THAT AT LEAST TWO
WILL BE OF THE SAME COLOUR.
LET'S TURN OFF THESE LIGHTS.
(CLAPPING)
GREAT. OH, BOY. THAT'S DARK.
(CAT YOWLING)
OH, SORRY, KITTY.
OKAY.
YOU KNOW, THIS IS WAY TOO DARK.
THIS ISN'T WORKING.
LET'S TURN THE LIGHTS BACK ON.
(CLAPPING)
LIGHTS?
(CLAPPING)
OH.
WELL, THAT DIDN'T WORK AT ALL.
(CHUCKLING)
I KNOW.
I'LL DO THIS BLINDFOLDED.
OKAY.
The man puts on a blindfold, then reaches into the drawer and pulls out socks.
He says, ONE, TWO, THREE.
ANY MATCHING COLOURS YET?
NO?
OKAY.
WELL, KEEP YOUR EYE ON
SOCK NUMBER...
...FOUR.
The man pulls out a second pink sock and says,
YES.
THE FIRST THREE SOCKS
WERE DIFFERENT COLOURS,
SO THE FOURTH ONE
HAS
TO MATCH.
IF YOU START WITH
THREE SOCK COLOURS,
PICKING FOUR SOCKS
GUARANTEES AT LEAST TWO SOCKS
OF THE SAME COLOUR.
AMAZING.
The man draws a yellow circle on a chalkboard, then taps the circle with his fist. The chalkboard becomes a monitor showing an animation of socks floating out of a dresser drawer.
The man says, THE LIKELIHOOD OF SOMETHING
HAPPENING,
LIKE CHOOSING
A SPECIFIC SOCK COLOUR,
IS CALLED PROBABILITY.
YOU CAN USE
THE SAME TRICK ON MITTENS, TOO.
TO GUARANTEE THAT YOU
FIND TWO MITTENS
OF THE SAME COLOUR IN THE DARK,
THE NUMBER OF MITTENS TO PICK UP
IS THE NUMBER OF MITTEN COLOURS
PLUS ONE.
THREE COLOURS, FOUR MITTENS.
Four mittens float above the dresser.
The man says, SO, THERE YOU HAVE IT.
I'VE SHARED YET ANOTHER
AMAZING SECRET:
HOW TO MATCH UP SOCKS
IN THE DARK.
TRY IT OUT YOURSELVES AT HOME.
BUT REMEMBER, USE CLEAN SOCKS.
(SNIFFING)
NOT SMELLY ONES.
PROBABILITY.
IT'S NOT MAGIC; IT'S MATH.
The drawer is full of socks. The Math Xplosion logo appears.
Text reads, produced by GAPC Entertainment. In association with TVO Kids. With the financial participation of Bell Fund, Canadian Media Fund and Shaw Rocket Fund.
The animated sun rises.
Vanessa says, WELCOME BACK.
LET'S PUT IT ALL TOGETHER NOW.
REVIEWING OUR DEFINITION
OF PROBABILITY,
THE LIKELIHOOD
OF SOMETHING HAPPENING.
WE'VE SHOWN IT THROUGH
A FRACTION AND NUMBER LINE.
AND WE USE PROBABILITY TO
MAKE DECISIONS AND PREDICTIONS,
ESPECIALLY THE WEATHER.
SO, THIS IS THE TIME FOR YOU
TO GET INVOLVED.
IF YOU HAVE THOSE MARKERS
AND THAT PAPER
AND DIFFERENT FORMS OF
PROBABILITY GAMES,
I WOULD LOVE FOR YOU
TO GET THAT READY
AND BRING IT TO YOUR WORK AREA.
AND WE ARE GOING TO
PLAY A LITTLE GAME.
SO, YOU, ON A PIECE OF PAPER,
WILL WRITE PROBABILITY EVENTS
THAT COULD HAPPEN IN WORDS.
OKAY?
SO, FOR EXAMPLE...
Vanessa places a green card on the tabletop display. It reads, “I win the lottery”.
Vanessa continues, ...MY FIRST POSSIBLE EVENT
THAT COULD HAPPEN?
I WIN THE LOTTERY.
OKAY? SO, I'M PICKING AN EVENT
THAT COULD HAPPEN.
AND THEN,
WHAT I'M GOING TO DO IS
THINK ABOUT THE LIKELIHOOD
OF IT OCCURRING. OKAY?
SO, YOU COULD THEN EXCHANGE
YOUR EVENT WITH A FRIEND,
MAYBE WITH A PARENT.
MAYBE TALK TO, UM,
ANOTHER ADULT IN YOUR LIFE,
LIKE A TEACHER.
ASK THEM WHAT ARE THE ODDS THAT
THEY'RE GOING TO WIN THE LOTTERY
THIS WEEK, AND THEN
PLOT IT ON YOUR NUMBER LINE.
Vanessa holds up the number line.
She continues, SO, IF I SAID TO MY TEACHER,
"MISTER OR MISS,
WHAT ARE THE ODDS
THAT YOU'RE GOING TO WIN
THE LOTTERY THIS WEEK?"
YOU CAN TELL THEM THAT,
IF THEY'RE UNSURE,
THAT IT WOULD BE SOMEWHERE
IN THIS RANGE
THAT THEY WIN THE LOTTERY.
OKAY? SO, THIS EVENT,
WE KNOW THAT OCCURS--
ONE OUT OF 33,000,000
ARE THE ODDS
OF WINNING THE LOTTERY.
SO, VERY, VERY UNLIKELY
THAT YOU WIN THE LOTTERY.
YOU COULD COME UP WITH
ANOTHER EVENT
THAT YOU COULD ASK YOUR FRIEND
MIGHT HAPPEN.
YOU FLIP A COIN
AND YOU LAND ON TAILS.
NOW, KNOWING WHAT YOU DO
ABOUT PROBABILITY,
YOU KNOW THAT YOU HAVE
AN EQUALLY LIKELY PROBABILITY,
ONE OVER TWO, BECAUSE TAILS--
THERE'S EITHER HEADS OR TAILS
AS THE POSSIBLE OUTCOMES,
AND YOU LAND ON TAILS.
SO, YOU'RE EQUALLY LIKELY, 50%.
AND THEN, WITH YOUR FRIEND
OR YOUR GUARDIAN OR PARENT,
THEY COULD PLOT THIS
ON THE NUMBER LINE.
I FLIP A COIN AND LAND ON TAILS.
NOW, YOU MIGHT WANT TO GET
SOME CERTAIN ONES IN THERE, TOO.
WE ALL ARE HOPING FOR THIS:
SUMMER WILL COME.
SO, YOU MAKE THAT EVENT
ON A PIECE OF PAPER.
YOU WRITE IT DOWN,
AND YOU ASK YOUR FRIEND,
"WHERE CAN IT BE PLACED
ON THE NUMBER LINE?"
IS THAT IMPOSSIBLE,
EQUALLY LIKELY, OR CERTAIN?
AND WE KNOW CERTAINLY,
EVERY SEASON
COMES WITHIN THE YEAR.
SO, IT'S CERTAIN THAT
THE SUMMER WILL COME,
AND THAT SUMMER BREAK
IS INEVITABLE.
OKAY? SO, WHAT WE'RE PRACTISING
WHEN WE DO THIS GAME,
WE'RE TALKING ABOUT
THE PROBABILITY
OF LIFE EVENTS HAPPENING.
AND ON OUR NUMBER LINE,
WE'RE PLOTTING THEM ON A SCALE
BETWEEN ZERO, HALF, AND ONE
AS OUR BENCHMARK NUMBERS.
OKAY? SO, THIS IS GETTING US
IN THE FRAME OF MIND
OF USING THESE TERMS
THAT WE'RE TALKING ABOUT,
PROBABILITY OF EVENTS.
Vanessa puts a green card on the display that reads, viewers are in grades 4, 5, and 6!
Vanessa says, OUR VIEWERS HERE
ARE IN GRADES 4, 5 AND 6.
THAT IS ALMOST CERTAIN.
OUR KEY DEMOGRAPHIC
FOR THIS VIDEO,
THE CURRICULUM,
IS IN THE JUNIOR GRADES.
SO, ALMOST CERTAINLY,
MANY OF OUR VIEWERS ARE--
MOST OF OUR VIEWERS
ARE, UM, IN THOSE GRADES.
BETWEEN LIKELY AND CERTAIN.
AND FINALLY, FOR A LAUGH,
"I LEARN HOW TO SKATEBOARD."
SO, KNOWING ME, I--
VERY HARD FOR ME TO LEARN THAT
AT MY AGE.
SO, THIS WOULD BE SOMETHING
THAT'S UNLIKELY
THAT I WOULD LEARN HOW TO DO.
SO, IF YOU KNEW SOMETHING ABOUT
YOUR FRIEND,
MAYBE THEY WOULD SAY,
"YOUR FAVOURITE FOOD IS CHIPS,"
FOR EXAMPLE.
AND YOU WOULD SAY,
"YOU KNOW WHAT? IT CERTAINLY IS.
YOU GOT THOSE ODDS RIGHT ON."
SO, YOU CAN WRITE
DIFFERENT LIFE EVENTS
AND SHARE THEM WITH A PARTNER
OR YOUR PARENTS
AND SEE WHERE THEY FALL
ON THE NUMBER LINE.
FOR YOUR SECOND GAME,
Vanessa puts a sheet of paper on the tabletop display.
She says, I WOULD LOVE FOR YOU TO USE
EITHER PLAYING CARDS,
SPINNERS, OR A DIE,
AND HONESTLY,
ALL CAN BE HOMEMADE
WITHIN A FEW MINUTES.
AND YOU'RE GOING TO STATE
A PROBABILITY TO WIN.
SO, IF I SAID I WANT TO MAKE
A GAME
THAT HAS A ONE-IN-FOUR
PROBABILITY TO WIN,
I WOULD MAKE A SPINNER
WITH FOUR SECTIONS ON IT.
IF I SAID I WANTED TO MAKE
A SPINNER--
OR SORRY, A GAME WITH A SPINNER
THAT HAS A PROBABILITY OF ONE
OUT OF SIX AFTER EVERY SPIN,
WE COULD MAKE A SPINNER
LIKE THIS ONE HERE
THAT HAS SIX SECTIONS.
OKAY? SO, IT'S UP TO YOU.
YOU CAN CHOOSE EITHER A SPINNER,
PLAYING CARDS, A DICE, COINS.
WHAT KIND OF GAME
WOULD YOU LIKE TO CREATE?
SO, FOR MY DICE GAME
THAT WE'RE GOING TO PLAY
A LITTLE BIT LATER,
IT'S CALLED MULTIPLY TO WIN.
I'M GOING TO ROLL MY TWO DICE,
AND THE ONLY WAY I CAN WIN
IS IF I ROLL TWO--
THE PRODUCT OF THE TWO ROLLS
HAS TO BE 36.
WHAT DOES THAT MEAN?
HOW CAN I GET 36
WHEN I MULTIPLY
MY TWO ROLLS TOGETHER?
IT MEANS THAT I'D HAVE TO HAVE
MY FIRST DICE, ROLL A SIX,
AND MY SECOND DICE,
ALSO ROLL A SIX.
Two brown dice sit on the table in front of Vanessa.
She says, BECAUSE SIX TIMES SIX
GIVES ME A PRODUCT OF 36.
WHAT ARE THE ODDS OF GETTING 36
AS MY PRODUCT?
WELL, I KNOW I HAVE
A ONE-OUT-OF-SIX CHANCE
OF ROLLING A SIX ON A DICE,
ON A SIX-SIDED DICE.
I ALSO AGAIN HAVE
A ONE-OUT-OF-SIX PROBABILITY
OF ROLLING A SIX
ON MY SECOND ROLL,
BECAUSE IT'S A SIX-SIDED DICE
DOWN HERE
AND THE NUMBER SIX
ONLY OCCURS ONE TIME.
WHEN I MULTIPLY
THOSE TWO NUMBERS TOGETHER,
ONE TIMES ONE IS ONE.
I MULTIPLY MY DENOMINATORS
TOGETHER.
SIX TIMES SIX IS 36.
SO, MY PROBABILITY
OF WINNING MY GAME
IS ONE OUT OF 36.
NOW, IF AGAIN, WE'RE USING IT
ON A NUMBER LINE,
I CAN SEE THAT
IT'S QUITE UNLIKELY
THAT I WILL WIN THIS GAME,
BUT WHY NOT HAVE FUN AND TRY?
SO, GO AHEAD
AND MAKE YOUR OWN GAME,
WHATEVER YOU CHOOSE,
WHATEVER YOU'D LIKE YOUR
PROBABILITY TO BE.
AND PLAY IT WITH A FRIEND,
A SIBLING, A PARENT, A GUARDIAN,
AND LET ME KNOW
HOW MUCH FUN YOU'RE HAVING.
The animated sun rises.
Vanessa continues, HOW ARE THE GAMES GOING?
ARE YOU HAVING A LOT OF FUN?
LET'S TRY MINE.
SO, WE HAD TALKED ABOUT
THEORETICAL PROBABILITY
BEING THE NUMBER OF FAVOURABLE
OUTCOMES
OVER THE NUMBER
OF POSSIBLE OUTCOMES.
AND WE KNOW IN MY GAME,
I REQUIRE BOTH NUMBERS
TO BE SIX,
SO THAT THEY MULTIPLY TO
A PRODUCT OF 36.
SO, I HAVE A ONE-IN-36
PROBABILITY
OF ME WINNING MY GAME.
SO, IT'S NOT VERY LIKELY,
BUT WHY NOT HAVE
A LOT OF FUN DOING IT?
SO, I'M GOING TO ROLL
MY FIRST DICE.
LET'S SEE WHAT I GET
AS MY FIRST.
Vanessa rolls a die and says, I GET A FIVE.
SO, UNFORTUNATELY,
I KNOW THAT NO MULTIPLICATION,
NO PRODUCT WITH A FIVE,
WILL EQUAL 36.
SO, I DIDN'T WIN
THAT FIRST TIME.
LET'S TRY IT AGAIN.
Vanessa rolls the die and says,
I GOT A FOUR.
SO AGAIN, UNFORTUNATELY,
I DIDN'T WIN.
BUT THE PROBABILITY TOLD ME
THAT IT'S VERY UNLIKELY
THAT I WOULD WIN.
OKAY? SO, I CAN MAKE A DECISION
BASED ON HOW LIKELY THE OUTCOME
IS TO HAPPEN GOING FORWARD.
SO, MAYBE AGAIN,
IF I WANTED TO REALLY BEAT
MY FRIENDS,
I COULD SAY, "YOU KNOW WHAT?
IF YOU ROLL TWO SIXES,
YOU CAN WIN," 'CAUSE I KNOW THAT
IT'S VERY, VERY DIFFICULT
FOR THEM TO WIN,
TO ROLL TWO SIXES.
SO, YOU CAN HAVE A LOT OF FUN
WITH YOUR FRIENDS THAT WAY, TOO.
AGAIN, WE'RE GOING TO USE
PROBABILITY IN OUR LIVES
TO MAKE DECISIONS
AND PREDICTIONS.
IF WE KNOW THAT THERE'S
A 10% CHANCE OF RAIN,
WE KNOW THAT IT'S VERY UNLIKELY
THAT YOU HAVE TO BRING
THAT UMBRELLA TO SCHOOL
THAT DAY.
COMPARED TO A 90% CHANCE
OF RAIN,
WHERE IT'S ALMOST CERTAIN
TO RAIN,
YOU'RE GOING TO NEED TO MAKE
A CHANGE OF PLAN
AND PACK THAT UMBRELLA
INTO THAT BACKPACK
BEFORE YOU GET IT--
AS YOU GO OFF TO SCHOOL.
Vanessa holds up the number line.
She says, USING THAT NUMBER LINE,
PLOTTING FROM IMPOSSIBLE
OR NEVER
ALL THE WAY TO CERTAIN, OKAY,
THIS IS GOING TO HELP YOU
UNDERSTAND
HOW LIKELY AN EVENT WILL OCCUR.
IN TERMS OF GAMES,
IN TERMS OF YOUR FAVOURITE TEAM
WINNING THE STANLEY CUP,
THEY'RE ALL EQUALLY AS LIKELY
TO WIN
AT THE BEGINNING OF THE SEASON.
The caption appears that reads, Junior 4-6. Teacher Vanessa.
Vanessa says, I HOPE YOU HAD A LOT OF FUN
WITH TODAY'S EPISODE.
I KNOW I DID. KEEP PRACTISING
THOSE POSITIVE AFFIRMATIONS.
KEEP PRACTISING
USING PHYSICAL ACTIVITY
AS A WARMUP TO GET YOU READY
FOR LEARNING AND EXPLORING,
AND I'LL CATCH YOU NEXT TIME
ON ANOTHER EPISODE
OF
TVOKIDS POWER HOUR
OF LEARNING.
(soft upbeat music plays)
Text reads, TVO kids would like to thank all the teachers involved in the Power Hour of learning as they continue to teach children of Ontario from their homes.
TVO Kids Power Hour of Learning. TVO. Copyright, The Ontario Educational Communications Authority 2021
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