00:01
All right, and your question, you're told that a, b, and c are evenly matched tennis players, and that a and b are going to play a match.
00:06
So i think this information here is going to be organized better in a tree diagram.
00:11
So i'm going to start with a tree diagram.
00:13
And the result of which is a wins, which i want to put a -w, or b wins.
00:20
And we're told they're evenly matched, so that probability occurs at 0 .5, 50 -50 chance.
00:26
Then whoever wins will play c so the next set of branches will go up here either a would win with 50 % chance or c would win with a 50 % chance and we continue this until one of the players has two wins so we already have a branch where a has two wins but there's other possibilities here that could occur if c won, then c is going to end up playing the player that was waiting, which would be b.
01:03
Now, c could win at a 0 .5 rate, or b could win at a 0 .5 rate.
01:12
Now, if c won, the game's over.
01:14
We don't go any further on these branches where we already have two wins.
01:19
But as you can see, the b branch, b only has one win now, and b would end up playing a.
01:25
Now, b could win the second time at 0 .5, which would end that branch.
01:32
We would have two bs or two wins for the b person, or a could win, and that would also end the branch, because that would be a second win.
01:45
Now, to find the probabilities of each of these branches, what we need to do is multiply out the branches.
01:50
So going out the top branch, 0 .5 times 0 .25 is 0 .25.
01:56
So that's our first branch.
01:58
The next branch, i'm just going to work my way down, would be 0 .5 to the third power, which would be 0 .125.
02:09
There were 3 .5s in that path.
02:14
Now, the next branch would be, these two are going to be equal because both branches have 4 .5s in them.
02:24
So 0 .5 to the 4th power will give you the probability for those branches.
02:32
0 .0 .0 .0625.
02:42
All right, that represents every possible outcome that started with a winning the first match.
02:48
Now we want to look at b.
02:50
Now, let's say b won that first match.
02:53
Then b is going to play c...