The last banana: A thought experiment in probability - Leonardo Barichello
-
0:06 - 0:11You and a fellow castaway
are stranded on a desert island -
0:11 - 0:14playing dice for the last banana.
-
0:14 - 0:16You've agreed on these rules:
-
0:16 - 0:17You'll roll two dice,
-
0:17 - 0:21and if the biggest number
is one, two, three or four, -
0:21 - 0:23player one wins.
-
0:23 - 0:28If the biggest number is five or six,
player two wins. -
0:28 - 0:30Let's try twice more.
-
0:30 - 0:33Here, player one wins,
-
0:33 - 0:36and here it's player two.
-
0:36 - 0:38So who do you want to be?
-
0:38 - 0:42At first glance, it may seem
like player one has the advantage -
0:42 - 0:46since she'll win if any one
of four numbers is the highest, -
0:46 - 0:47but actually,
-
0:47 - 0:54player two has an approximately
56% chance of winning each match. -
0:54 - 0:58One way to see that is to list all
the possible combinations you could get -
0:58 - 1:00by rolling two dice,
-
1:00 - 1:03and then count up
the ones that each player wins. -
1:03 - 1:05These are the possibilities
for the yellow die. -
1:05 - 1:08These are the possibilities
for the blue die. -
1:08 - 1:13Each cell in the chart shows a possible
combination when you roll both dice. -
1:13 - 1:15If you roll a four and then a five,
-
1:15 - 1:17we'll mark a player two
victory in this cell. -
1:17 - 1:22A three and a one gives
player one a victory here. -
1:22 - 1:25There are 36 possible combinations,
-
1:25 - 1:28each with exactly the same
chance of happening. -
1:28 - 1:31Mathematicians call these
equiprobable events. -
1:31 - 1:35Now we can see why
the first glance was wrong. -
1:35 - 1:37Even though player one
has four winning numbers, -
1:37 - 1:40and player two only has two,
-
1:40 - 1:44the chance of each number
being the greatest is not the same. -
1:44 - 1:49There is only a one in 36 chance
that one will be the highest number. -
1:49 - 1:53But there's an 11 in 36 chance
that six will be the highest. -
1:53 - 1:56So if any of these
combinations are rolled, -
1:56 - 1:57player one will win.
-
1:57 - 2:00And if any of these
combinations are rolled, -
2:00 - 2:01player two will win.
-
2:01 - 2:04Out of the 36 possible combinations,
-
2:04 - 2:1016 give the victory to player one,
and 20 give player two the win. -
2:10 - 2:12You could think about it this way, too.
-
2:12 - 2:14The only way player one can win
-
2:14 - 2:19is if both dice show
a one, two, three or four. -
2:19 - 2:22A five or six would mean
a win for player two. -
2:22 - 2:27The chance of one die showing one, two,
three or four is four out of six. -
2:27 - 2:31The result of each die roll
is independent from the other. -
2:31 - 2:34And you can calculate the joint
probability of independent events -
2:34 - 2:36by multiplying their probabilities.
-
2:36 - 2:41So the chance of getting a one, two,
three or four on both dice -
2:41 - 2:46is 4/6 times 4/6, or 16/36.
-
2:46 - 2:48Because someone has to win,
-
2:48 - 2:55the chance of player two winning
is 36/36 minus 16/36, -
2:55 - 2:57or 20/36.
-
2:57 - 3:01Those are the exact same probabilities
we got by making our table. -
3:01 - 3:04But this doesn't mean
that player two will win, -
3:04 - 3:09or even that if you played 36 games
as player two, you'd win 20 of them. -
3:09 - 3:13That's why events like dice rolling
are called random. -
3:13 - 3:16Even though you can calculate
the theoretical probability -
3:16 - 3:17of each outcome,
-
3:17 - 3:22you might not get the expected results
if you examine just a few events. -
3:22 - 3:26But if you repeat those random events
many, many, many times, -
3:26 - 3:30the frequency of a specific outcome,
like a player two win, -
3:30 - 3:33will approach its theoretical probability,
-
3:33 - 3:36that value we got by writing down
all the possibilities -
3:36 - 3:39and counting up the ones for each outcome.
-
3:39 - 3:43So, if you sat on that desert island
playing dice forever, -
3:43 - 3:47player two would eventually
win 56% of the games, -
3:47 - 3:50and player one would win 44%.
-
3:50 - 3:54But by then, of course, the banana
would be long gone.
- Title:
- The last banana: A thought experiment in probability - Leonardo Barichello
- Description:
-
View full lesson: http://ed.ted.com/lessons/the-last-banana-a-thought-experiment-in-probability-leonardo-barichello
Imagine a game of dice: if the biggest number rolled is one, two, three, or four, player 1 wins. If the biggest number rolled is five or six, player 2 wins. Who has the best probability of winning the game? Leonardo Barichello explains how probability holds the answer to this seemingly counterintuitive puzzle.
Lesson by Leonardo Barichello, animation by Ace & Son Moving Picture Co, LLC.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 04:10
Jessica Ruby approved English subtitles for The last banana: A thought experiment in probability - Leonardo Barichello | ||
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Jessica Ruby edited English subtitles for The last banana: A thought experiment in probability - Leonardo Barichello | ||
Jessica Ruby edited English subtitles for The last banana: A thought experiment in probability - Leonardo Barichello | ||
Jessica Ruby accepted English subtitles for The last banana: A thought experiment in probability - Leonardo Barichello | ||
Jessica Ruby edited English subtitles for The last banana: A thought experiment in probability - Leonardo Barichello | ||
Jessica Ruby edited English subtitles for The last banana: A thought experiment in probability - Leonardo Barichello | ||
Jennifer Cody edited English subtitles for The last banana: A thought experiment in probability - Leonardo Barichello |