00:01
We are told that three men toss coins to see who pays for coffee.
00:04
If all three match, they have to toss again.
00:07
But otherwise, the odd man pays for the coffee.
00:11
So let's first calculate the probability on a given toss that all three match.
00:33
So this is equal to the number of ways to match, divided by the total number of outcomes.
00:47
And so this is equal to the number of ways to match.
00:51
There is only two ways.
00:52
They can all be heads or they can all be tails.
00:54
So that's 2.
00:57
And the total possible number of outcomes, each coin has two options and there are three coins.
01:03
So it's 2 to the exponent 3, which is 8, or 1 out of 4.
01:17
So for part a, the probability that they need to do this more than once is equal to the probability that all three coins match on the first toss.
01:40
So it's 1 out of 4.
01:43
And then for b, the probability that they need to do this.
01:47
At most twice, this is equal to the probability that the first toss is not all matches.
02:12
So that's the way it ends on the first toss, plus the probability that it ends on the second toss, given that it did not end on the first toss.
02:43
The probability that at most two tosses are necessary is the probability that the game ends on the first toss, which only happens if they don't all match, plus the probability that the game ends on the second toss, given that it did not end on the first toss.
03:06
And so the first term here, probability that the first toss is not all matches, is one minus the probability that all three coins do match...