00:01
In this problem, two athletic teams play a series of games.
00:04
The first team to win four games is declared the overall winner.
00:09
For party a, we suppose that one of the teams is stronger than the other and wins each game with a probability of 0 .6.
00:19
Independently of the outcomes of the other games, of course.
00:22
We want to find the probability that the stronger team wins the series.
00:27
Suppose we have a series of end games.
00:36
See the probability that the stronger teams won first it might win from the first four games and this needs a probability 0 .6 to the bar of 4 and it might win after 5 games and this needs a probability of 0 .6 to the bar of 4 because the stronger wins the 4 multiplied by 0 .4 to the bar of 1 because the weaker team wins 1 one game out of these five.
01:09
But this might happen with total number of combinations.
01:14
This total number of combinations is 5 minus 1, choose 3.
01:22
And we still go in this direction until we reach the end games.
01:30
We sum these probabilities, then we can get the probability that the winner team, the stronger teams wins the series...