00:01
An urn contains five balls with one marked win and four marked lose.
00:06
And you and another player take turns selecting a ball at random from the urn, one at a time.
00:12
The first person to select win is the winner.
00:16
And we are asked, if you draw first, find the probability that you will win if sampling is done with replacement and without replacement.
00:25
So for part a, it's with replacement.
00:28
So you are drawing first.
00:29
So the probability that you win, well one way to win, let's just call the probability of win.
00:37
One way to win is to get the win ball on the first draw.
00:42
There's only one out of five balls that are marked win, so the probability of getting it on the first draw is one out of five.
00:51
Another way to win is for you to not win on the first draw, and your opponent to also not win on his or her first draw, but then you win on your second draw.
01:01
Draw.
01:02
So for you to not win on the first draw, you have to get one of the lose balls, a 4 out of 5 probability of that.
01:10
And then your opponent has to get one of the lose balls.
01:12
There's 4 balls left, 3 of which say lose on them, so there's a 3 quarter chance of your opponent losing, or not winning on that draw.
01:24
Then there are 3 balls left, one of which is the win.
01:29
So this product here represents the probability of winning the second time you draw or you could win on the third draw your third draw so once again we have to go through the process of you getting a lose ball on the first draw your opponent getting a lose ball on the second draw and then on the third draw you have to get a lose ball so there's a two -thirds chance of that then your opponent's second draw there's two balls left one is lose and then you draw a third third time, there's only one ball left, it's the win ball...