Transcript: Challenge #8 | Mar 26, 1999

Mister C stands in the studio by a table. He’s in his mid-forties, with a dark beard and wavy black hair. He’s wearing glasses, a white T-shirt with a motif and a dark blue jacket.

He says HI!
I'M PLAYING WITH ONE OF
MY FAVOURITE OBJECTS.
THIS IS A SINGLE DIE AND THERE
ARE MANY, MANY, MANY KINDS OF
DICE BUT THIS IS THE STANDARD
SIX-SIDED CUBIC DIE.
PROBABILITY HAS ALWAYS BEEN
ONE OF MY FAVOURITE TOPICS.
WHAT I WANT TO TALK A LITTLE
BIT ABOUT IS THE DIFFERENCE
BETWEEN FINDING A THEORETICAL
PROBABILITY, WHICH WE'LL DO A
LITTLE BIT ABOUT WITH,
AND DOING AN EXPERIMENTAL
PROBABILITY AND WHEN
YOU USE EITHER CASE.
THE FIRST THING THAT I'M
CONCERNED ABOUT IS IF I TAKE
A STANDARD DIE LIKE THIS,
I LOOK AT IT, IT LOOKS
PRETTY REGULAR.
AND THIS ONE IS A PERFECT
CANDIDATE PROBABLY FOR A
THEORETICAL APPROACH.
BUT I WANT TO DO AN EXPERIMENT
FIRST JUST TO SEE IF IT'S OKAY.
WHAT I NEED TO DO TO DO AN
EXPERIMENT IS TO SET UP A TALLY.
THE TALLY THAT I HAVE HERE,
IS PRETTY STANDARD STUFF.

A blue sheet of paper shows four columns. They read “Outcome, Tally, Frequency, Relative Frequency.” A row at the bottom reads “Totals.”

He continues FIRST OF ALL, IN THE FIRST
COLUMN I HAVE TO LIST ALL THE
POSSIBLE OUTCOMES.
WITH THE STANDARD SIX-SIDED
DIE NUMBERED THE WAY IT IS,
I'LL LIST ONE, TWO,
THREE, FOUR, FIVE, SIX.
OBVIOUSLY IF IT'S A DIFFERENCE
SIZED DIE OR SOMETHING ELSE,
THIS MIGHT BE
SOMEWHAT DIFFERENT.
THIS IS FOR THE TALLY WHEN I
ACTUALLY DO THE EXPERIMENT.
WELL YOU KNOW, I MAYBE I
SHOULD DO IT A FEW TIMES
JUST TO GET A SENSE OF WHAT
WE'RE GOING TO GET HERE.
He rolls the die and continues OH, I GOT A THREE.
AND I'VE GOT A SIX.
AND I'VE GOT A ONE.
I'LL DO THIS A
COUPLE MORE TIMES.
I GOT ONE AGAIN.
AND I'VE GOT A FIVE.

He writes those numbers under the Tally column.

He continues THE FREQUENCY COLUMN IS, ONCE
YOU'VE DONE ALL THIS, AS YOU
CAN SEE THAT NUMBER
ONE OCCURRED TWICE.
THE NUMBER TWO DIDN'T
OCCUR SO I CAN PUT ZERO.
NUMBER THREE OCCURRED ONCE.
NUMBER FOUR DID NOT OCCUR.
FIVE ONCE, SIX ONCE AND IF I
ADD ALL THESE UP IT'S EQUAL TO
THE NUMBER OF
TRIALS THAT I RAN.

He writes “5” next to “Totals.”

He continues THE RELATIVE FREQUENCY IS A
VERY INTERESTING NUMBER AS
WELL BECAUSE QUITE OFTEN WHEN
WE DO HISTOGRAMS, WE WANT THE
RELATIVE FREQUENCY.
AND WHAT YOU DO TO GET THAT
IS TO TAKE THE FREQUENCY AND
DIVIDE IT BY THE TOTAL.
SO IN THIS CASE...
IF YOU'VE DONE THIS CORRECTLY
AND ADD UP THE DECIMALS
YOU SHOULD GET 1.0
WHICH I DO IN THIS CASE.
WITH THAT DIE, IF I DID THIS,
I MEAN A REALLY, REALLY
CRITICAL QUESTION IS HOW
MANY TIMES DO YOU DO IT
IN THE SPAN OF?
IS FIVE TIMES ENOUGH TO KNOW
THAT THAT'S A FAIR DIE,
THAT EVERY SIDE WILL COME
UP, MORE OR LESS EQUALLY?
NO.
I MIGHT SUGGEST 100 AND
THAT MIGHT BE REASONABLE.
MAYBE EVEN MORE.
IF I WERE TO DRAW A HISTOGRAM
AND I HAD DONE IT ENOUGH TIMES.
A HISTOGRAM IS
LIKE A BAR GRAPH.
WE HAVE ONE, THESE ARE THE
OUTCOMES ALONG THE BOTTOM.
AND ON THIS SIDE I WOULD BE
DOING THE RELATIVE FREQUENCIES.

As he speaks, he draws the graph.

He continues AND THOSE WOULD BE DECIMALS.
I'M NOT GOING TO ACTUALLY FILL
IN THE VALUES.
BUT IF I DID THIS ENOUGH
TIMES THE HISTOGRAM WOULD LOOK
VERY MUCH LIKE A RECTANGLE
SOMETHING LIKE THAT.
IN OTHER WORDS, IT WOULD BE
VERY EVEN ALONG THE TOP.
WOULD IT BE EXACTLY EVEN?
NO, I DON'T THINK SO BECAUSE
EVEN THOUGH THE DIE WILL ACT
RELATIVELY FAIRLY, IT DOESN'T
REMEMBER WHAT EXACTLY IT DID
BEFORE AND IT CAN'T EVEN
ITSELF UP SO THERE'LL BE
SOME DIFFERENCES.
BUT ENOUGH TIMES AND IT'LL
LOOK SOMETHING LIKE A RECTANGLE.
WELL, WHAT IF I DID A SLIGHTLY
DIFFERENT EXPERIMENT INVOLVING
SIX-SIDED DICE AND ROLLED A
PAIR OF THEM AND I ADDED
THEIR TOTALS?
SO IN THIS CASE I WOULD'VE HAD
FOUR, IF I ROLL AGAIN I'LL
JUST.... I GET FOUR AGAIN.
A LITTLE BIT OF A SURPRISE.
I GET ELEVEN.
WHAT WOULD THE GRAPH OF
THAT PARTICULAR KIND OF
EXPERIMENT BE?
IF I DID IT ENOUGH TIMES,
YOU'LL FIND THAT THE HISTOGRAM
WILL BE KIND OF A STEP
HISTOGRAM LIKE THIS.
AND THEN COME BACK
DOWN THE OTHER WAY.
NOW I DON'T KNOW IF I'VE DONE
IT ENOUGH TIMES BUT, IF YOU
WERE TO LOOK AT THE
CHARACTERISTIC SHAPE OF THAT
GRAPH, IT WOULD BE A VERY
DEFINITE ISOSCELES TRIANGLE.
WELL, THOSE KINDS OF
EXPERIMENTS, I WOULD SAY
UNEQUIVOCALLY, ONE COULD
PRETTY MUCH USE A THEORETICAL
PROBABILITY TO MAKE GUESSES
ABOUT HOW OFTEN THOSE THINGS
WOULD OCCUR.
HERE'S ANOTHER SIX-SIDED DIE.

He places a black die on the paper.

He continues THAT LOOKS PRETTY
STANDARD TO ME.
SIX SIDES, HAS ALL
THE NUMBERS ON IT.
I'M GOING TO DO AN
EXPERIMENT WITH IT AS WELL.
SET-UP MY OUTCOMES AGAIN.

On a new Tally paper, he writes “1,2,3,4,5,6” under the Outcome column.

He continues LET'S SEE WHAT I...
OH, I GOT A THREE.
I'LL DO THAT AGAIN.
OH, I GOT A THREE AGAIN,
THAT'S A BIT OF A SURPRISE.
I GOT THREE AGAIN.
OH, I GOT A SIX.
OH, I GOT A THREE AGAIN.
I'M GOING TO --
THIS IS STRANGE!
I GOT THREE AGAIN.
AND AGAIN!
OH, MY GOODNESS AND AGAIN!
OH, I GOT A TWO.
AND NOW I'LL DO IT ONE MORE
TIME LET'S SEE WHAT HAPPENS.
WHOOPS, THERE IT IS.
IT CAME OUT THREE AGAIN.
IF I WERE TO DO THE
FREQUENCIES HERE
I’D BE 0,1,8,0,0,1.
AND THE RELATIVE
FREQUENCY 0, THIS IS
ONE OUT OF TEN EQUAL TO
.1, EIGHT OUT OF 10 EQUAL .8,
ZERO, ZERO, ONE OUT OF TEN
EQUAL TO .1
YOU KNOW SOMETHING, I THINK
THERE'S SOMETHING WRONG WITH
THAT DIE.
THIS IS A REALLY GOOD EXAMPLE
OF WHY EXPERIMENTS ARE USED.
SOMETIMES IT DETECTS WHETHER
A DIE IS A FAIR DIE OR NOT.
THIS IS CLEARLY
NOT A FAIR DIE.
YOU'LL SEE THAT IF YOU
WATCH HOW THAT BOUNCES...
NOW SOMETIMES IT GOES
OVER ON THE SIDE.
BUT MORE OFTEN THAN NOT IT
COMES UP ON THAT THREE BECAUSE
IT'S WEIGHTED ON THE FAR SIDE.
OKAY, SO WE FOUND ONE GOOD
REASON FOR DOING EXPERIMENTS.
LET'S LOOK AT SOME
OTHER REASONS.
GOING BACK TO ANCIENT TIMES,
THEY USED SHELLS FOR GAMBLING.
THESE ARE CALLED COWRY SHELLS.

He puts two dark cowry shells on the paper.

He continues AND WE COULD SAY THAT WHEN
THEY'RE LIKE THIS, IF YOU LOOK
AT THE SHELL YOU'LL NOTICE
THAT IT'S KIND OF LIKE A FIST.
LIKE THIS, I'LL PUT IT UP.
IT'S KIND OF LIKE MY FIST.
WELL, WE'LL SAY THAT THIS IS
FIST DOWN AND THIS IS FIST UP.
NOW THE QUESTION I HAVE IS
IS IT LIKE FLIPPING A COIN?
IS IT 50 PERCENT DOWN
AND 50 PERCENT UP?
OR IS IT SOMETHING ELSE?
WELL I'M GOING TO GRAB A WHOLE
BUNCH OF THESE AND ROLL THEM
ON THE TABLE AND SEE.
I'LL SET MY TALLY
UP HERE, TOO.
I HAVE FIST UP...
AND FIST DOWN.
SO, LET'S SEE
WHAT HAPPENS HERE.
He rolls six cowry shells and continues
LET'S SEE, IT'S THREE AND
THREE IN THIS PARTICULAR CASE.
I'M GOING TO DO THIS
A COUPLE MORE TIMES.
OH, THIS TIME IT'S
FIVE AND ONE.
SO THAT WAS ONE FOR THIS ONE...
AND FIVE FOR THAT ONE.
LET'S DO THAT AT LEAST ONE
MORE TIME AND SEE WHAT HAPPENS.
WHOOPS, LET'S SEE
WHAT WE HAVE HERE.
THIS TIME IT'S PLUS
FOUR AND PLUS TWO.
AND ONE MORE TIME I CAN
SET A FEW IN THERE
AND SEE WHAT HAPPENS.
WE GOT FOUR OF
THOSE AND TWO.
NOW LET'S SEE WHAT
WE HAVE AS A TOTAL.
THAT'S 12 AND THIS
ONE IS ALSO 12.
YOU KNOW SOMETHING, BASED
ON THIS LIMITED AMOUNT OF
INFORMATION I MIGHT EVEN
SUGGEST THAT IT'S 50-50.
BECAUSE, AS YOU CAN SEE, THIS
AT 50 PERCENT OF THE TIME
AND THIS ONE IS 50
PERCENT OF THE TIME.

He writes those percentages under the Relative Frequency column.

He continues QUESTION AGAIN IS
THIS ENOUGH TIMES?
DOES THIS TELL YOU
THE WHOLE STORY?
I CAN SUGGEST TO YOU THAT IF
YOU DO THIS, SAY, 500 TIMES
THAT THESE TWO PERCENTAGES ON
HERE, WILL ACTUALLY DIVERGE
QUITE A BIT FROM
50 PERCENT EACH.
ONE OF THE KEY THINGS HERE IS
NO PHYSICIST CAN PREDICT JUST
BY DOING SOME EQUATIONS
WHETHER IT'S 50 PERCENT,
50 PERCENT OR SOMETHING ELSE.
IT IS TOO COMPLICATED
AN OBJECT.
LET'S GO TO ONE MORE
OBJECT AS AN EXAMPLE.
GET ANOTHER TALLY
SHEET OUT HERE.
THIS ONE IS A SIX-SIDED
OBJECT AS WELL.
AS YOU CAN SEE, I'LL
ROTATE IT AROUND...
IT'S A RECTANGULAR PRISM.

The wooden rectangular prism shows numbers on the sides.

He continues CERTAINLY NOT NEAR A CUBE.
I THINK THAT ANY ONE OF US CAN
TELL THAT IT'S MORE LIKELY
THAT IT'LL END UP ON ONE OF
THESE SIDES THAN IT WILL
THIS WAY.
Showing the side with number 5 on it, he continues IS IT IMPOSSIBLE
TO END UP THIS WAY?
WELL, I WOULD SAY NOT.
YOU CAN DO AN
EXPERIMENT AGAIN.
WHAT A PHYSICIST WILL TELL YOU
IS THAT, AGAIN, THEY CAN'T
PREDICT JUST USING FORMULAE
WHETHER IT IS MORE LIKELY OR
WHAT THE PERCENTAGE LIKELIHOOD
IS THAT IT WILL COME UP THIS
WAY AS COMPARED TO THAT WAY.
WHAT THEY WOULD DO IS THEY'D
SAY, BETTER DO AN EXPERIMENT.
SO WE CAN DO THAT AS
WELL WITH THIS ONE.
ONE, TWO, THREE,
FOUR, FIVE, SIX.
I'M GOING TO ROLL IT SAY FIVE
TIMES AND SEE WHAT HAPPENS HERE.
NOW THESE ARE ALL THE LONG
SIDES, AND THESE ARE ALL THE
SMALL PARTS.
WELL IN THIS PARTICULAR
CASE WE COULD WORK OUT THE
FREQUENCIES.
FIVE TOTAL TRIALS.
AGAIN, WE GET 20 PERCENT HERE,
20 PERCENT HERE, 20 PERCENT
HERE, 40 PERCENT HERE.
BUT YOU KNOW THAT EXPERIMENT
WE HAVEN'T DONE IT ENOUGH TIMES
REALLY AGAIN TO FIND OUT IF IT
WOULD EVER END UP THIS WAY.
AND I WILL SUGGEST TO YOU, IF
YOU DO THIS 200 TIMES IT WILL
END UP ON THE FIVE SOMETIMES
AND IT WILL END UP ON THE SIX
SOMETIMES.
THAT LOOKS LIKE A NINE.
I'LL ROTATE IT AROUND...
IT'S A SIX.
SO, ANOTHER GOOD EXAMPLE OF A
PLACE WHERE YOU WOULD USE AN
EXPERIMENT TO FIND
THE PROBABILITIES.
HOW ABOUT THIS OBJECT?
OR THESE INTERESTING OBJECTS?

He places two black dice and two white and blue ceramic pieces on the table.

He continues THEY'RE ALL CUBIC.

Holding the die, he says AND IF WE WERE TO NUMBER THE
SIDES, YOU CAN SEE THAT
THIS IS NOT A PURE CUBE.
ANOTHER PLACE FOR EXPERIMENTS.
THESE ARE LIKE THE SHELLS.
THEY'RE LITTLE STONES.
WOULD THEY ACT LIKE A COIN
50-50 OR WOULD THEY BE MORE
LIKE THE SHELLS?
AGAIN, AN EXPERIMENT WOULD
BE WORTH TRYING IF YOU WERE
CURIOUS ABOUT THESE THINGS.
NOW, YOUR CHALLENGE OVER THE
NEXT WEEK OR SO WILL BE TO DO
A COUPLE EXPERIMENTS.
THEY DON'T INVOLVE
OBJECTS LIKE THESE.
THEY'RE SLIGHTLY DIFFERENT.
THE FIRST ONE, I'M GOING TO
PULL IN WHAT YOU'RE USING
FOR THE EXPERIMENT.
YOU'LL NEED A PARTNER AND IF
YOU DO IT AT HOME, MAYBE JUST
A PARENT OR A SIBLING.
AND WHAT YOU NEED TO DO IS
CUT SIX PIECES OF STRING.
EXACTLY THE SAME LENGTH.

He holds six pieces of yellow ribbon.

He continues I WOULD SAY THIS IS A LITTLE
BIT EXTRA-LONG, BUT PROBABLY
ABOUT THAT LONG MORE OR LESS.
WHAT YOU THEN DO IS YOU TAKE
THE STRING AND YOU TAKE THEM
IN PAIRS AND TIE THEM
TOGETHER LIKE THIS.
SO I'VE ALREADY
DONE TWO PAIRS.
THEY'RE READY TO GO AND I'M
GOING TO DO THE THIRD PAIR
JUST TO DEMONSTRATE.
SO YOU TAKE THE END AND...
ASSUMING I DON'T MESS UP
TOO MUCH HERE.
TIE THEM TOGETHER LIKE THAT.
NOW, HERE'S THE TRICK, YOU
TAKE THE KNOTS, THREE KNOTS,
MIX UP THE STRINGS AT THE
BOTTOM, CLOSE THEM IN YOUR
FIST LIKE THIS AND THEN YOU
ASK YOUR PARTNER TO RANDOMLY
CHOOSE PAIRS OF STRING AND TIE
THEM TOGETHER AT THE BOTTOM.
SOMETHING LIKE THIS.
AND LET'S SEE, I'LL PICK THOSE
AND I'LL TIE THEM TOGETHER.
SO YOU END UP WITH THREE
KNOTS ON THE BOTTOM AS WELL.
NOW REMEMBER, SOMEBODY ELSE IS
DOING THIS, YOU'RE NOT DOING
IT YOURSELF.
THE PROBLEM WITH THAT IS
IF YOU DO IT YOURSELF,
YOU'VE GOT A BIT OF A BIAS.
YOU MAY TRY TO MAKE IT TO
WORK THE WAY YOU WOULD
LIKE IT TO WORK.
IF SOMEBODY ELSE IS DOING IT
RANDOMLY THEN IT'S A VERY
WORTH-WHILE EXPERIMENT.
THE QUESTION IS WHAT WILL
HAPPEN WHEN I LET GO OF MY
FIST AFTER I'VE DONE THAT?
TIED THREE SETS AT THE BOTTOM,
I LET GO OF IT, THERE'S GOING
TO BE SOME KIND
OF ARRANGEMENT.

He opens his hand and the strings fall on the table.

He continues I'M NOT GOING TO SHOW YOU.
PARTLY BECAUSE ONE OF YOUR
CHALLENGES IS TO LIST ALL THE
POSSIBLE WAYS THAT THOSE
STRINGS CAN BE CONNECTED
WHEN YOU'RE FINISHED.
I WANT YOU TO DO THAT
EXPERIMENT WITH SOMEBODY ELSE
AT LEAST 10 TIMES.
FROM THAT, I WANT YOU TO
PREDICT WHICH ONES OF THE
OUTCOMES ARE MORE LIKELY,
WHICH ONES OF THE OUTCOMES
ARE LESS LIKELY.
THE ONLY OTHER EXPERIMENT THAT
YOU HAVE TO DO -- AND IT'S NOT
A TERRIBLY DIFFICULT ONE,
BUT IT'S BASED ON A VERY
INTERESTING CONCEPT.
YOU KNOW YOU'VE BEEN IN THE
SUPERMARKET BEFORE AND YOU'VE
LOOKED AT CEREAL BOXES.
CERTAINLY YOUR YOUNGER
SIBLINGS MIGHT BE INTERESTED
IN THIS.
AND YOU SEE ON A CEREAL BOX
'COLLECT ALL FOUR' MAYBE
POSTERS OF ROCK GROUPS, MAYBE
STAR TREK CHARACTERS, MAYBE
HOCKEY PLAYERS, WHO KNOWS.
PERHAPS IT'S SIX DIFFERENT
THINGS, PERHAPS IT'S EIGHT.
WELL, GET ALL SIX, GET
ALL FOUR, GET ALL TWELVE.
THE QUESTION I HAVE HERE IS,
HOW MANY BOXES OF CEREAL DO
I NEED TO BUY IN TOTAL, TO
PROBABLY GET ALL THE CARDS
OR THE POSTERS OR WHATEVER?

A blue sheet of paper reads “Get all 6,4,12,20.”

He continues WELL, WE NEED TO SIMULATE AN
EXPERIMENT AND THIS METHOD IS
CALLED THE MONTE CARLO METHOD
BECAUSE IT EMPLOYS DICE
I WOULD THINK.
IF IT'S A COLLECT ALL SIX THEN
I WOULD USE A SIX-SIDED DIE.
IF IT SAYS COLLECT ALL FOUR
THEN I WOULD USE A TETRAHEDRON,
OR A FOUR-SIDED DIE.
IF IT SAYS COLLECT ALL TWELVE,
I WOULD USE A DODECAHEDRON
OR A TWELVE-SIDED DIE.
IF IT SAYS COLLECT ALL TWENTY,
I WOULD USE THE ICOSAHEDRON,
THE 20-SIDED DIE TO
SIMULATE THE EXPERIMENT.
As he mentions them, he places those objects next to the numbers of the “Get all” paper.

He continues LET ME SHOW YOU WHAT I MEAN.
WE'RE GOING TO SAY THAT THE
PARTICULAR BOX OF CEREAL THAT
WE'RE LOOKING AT IS
'COLLECT ALL FOUR POSTERS.'
SO HERE'S WHAT MY
TALLY WOULD LOOK LIKE.

A new handwritten sheet of paper under the title “Tally. Get all 4” appears. It shows six columns. They read “Trial numbers, 1, 2, 3, 4, Total rolls.”

He continues THE TRIAL NUMBERS, WHICH
WOULD GO DOWN HERE.
TRIAL ONE, TWO, THREE AND IF
YOU WERE DOING TWENTY TRIALS
THERE WOULD BE TWENTY OF
THESE ROWS, 10 WHATEVER.
IF IT'S COLLECT ALL FOUR THEN
YOU'LL HAVE COLUMNS FROM ONE,
TWO, THREE AND FOUR, IF IT WAS
SIX YOU WOULD HAVE A COUPLE
MORE COLUMNS.
WHAT I HAVE TO DO AND OF
COURSE I'M MAKING TWO PRETTY
IMPORTANT ASSUMPTIONS HERE,
NUMBER ONE I'M ASSUMING THAT
THE CARDS OR THE POSTERS OR
WHATEVER IT IS IN THE CEREAL
BOX ARE IN THE
BOXES RANDOMLY.
SO THAT'S PRETTY IMPORTANT.
AND THE SECOND THING I'M
ASSUMING IS THAT YOU'RE NOT
TRADING WITH YOUR FRIENDS.
SO, WHAT I'M GOING TO DO FOR
ANY GIVEN TRIAL IS I'M GOING
TO ROLL A DIE, IN THIS CASE
THE FOUR-SIDED DIE, AND I'M
GOING TO ROLL AND COUNT EVERY
TIME IT TAKES UNTIL I GET AT
LEAST ONE OF EACH NUMBER.
HERE IT GOES!
HEY, I'VE GOT TWO
PRIZES ALREADY.
I'M DOING GREAT.
NOW HOW MANY BOXES OF CEREAL?
WELL, IN THIS CASE IT LOOKS
LIKE IT WOULD'VE TAKEN ME FIVE.
LET'S DO THAT AGAIN.
BOY, I'M BUYING MORE AND
MORE CEREAL THIS TIME.
NOW WE'VE GOT THEM ALL.
I TOOK ONE, PLUS THREE IS
FOUR, PLUS TWO IS SIX,
IT TOOK ME SEVEN BOXES OF
CEREAL TO GET THEM ALL.
I'M GOING TO DO THE
EXPERIMENT ONE MORE TIME.
AMAZINGLY, AGAIN
IT ONLY TOOK FIVE.

He writes all the results he gets as he rolls the die.

He continues NOW LET'S SAY YOU DID THIS
PARTICULAR EXPERIMENT 10 TIMES.
WELL, I'M GOING TO USE MY
ACTUAL DATA FROM HERE.

On a new piece of paper, he writes “5 plus 7 plus 5.” The equation continues “plus 7 plus 12 plus 11 plus 5 plus 9 plus 21 plus 9 equal (blank space).”

He continues SO THERE ARE 10 DIFFERENT
TRIALS, WE CAN COUNT THEM UP,
AND THE TOTAL IS, I ALREADY
KNOW THAT THESE CHUNK IS 74
PLUS 10 MORE IS
84, PLUS 7 IS 91.
IF I DIVIDE, IT'S 9.1 OR
ABOUT 9 BOXES OF CEREAL...
ON AVERAGE TO GET
ALL FOUR PRIZES.
YOUR CHALLENGE IS, IN YOUR
CLASS, TO SIMULATE DIFFERENT
EXPERIMENTS FOR DIFFERENT
NUMBERS OF PRIZES.
YES, YOU WILL NEED A VARIETY
OF DIFFERENT KINDS OF DICE,
BUT THEY'RE EASILY AVAILABLE.
AND ACTUALLY IF YOU GO TO A
GAME STORE PROBABLY YOU'LL BE
ABLE TO QUITE EASILY GET ONE
OF EACH OF THESE DIE.
SO, YOUR CHALLENGE IS
TO DO TWO EXPERIMENTS.
ONE INVOLVING THE STRING
AND ONE INVOLVING THE
MONTE CARLO METHOD.
WE'LL TALK TO YOU LATER.
WE'LL SEE YOU AT
THE NEXT PROGRAM,
AND I WISH YOU THE BEST OF
LUCK WITH YOUR EXPERIMENTS.

Watch: Challenge #8