Jack N. answered • 04/05/22
Statistics Tutor
Interesting question!
From the question, we know that the underdog has a .45 probability of winning any individual game. With this information, we can calculate the probability that the underdog wins a 4, 5, 6, or 7 game series.
First, let’s ask ourselves how many ways can the underdog win. The underdog may win if the team wins the first 4 games, 4 of the first 5 games, 4 of the first 6 games, or 4 of the 7 games.
The probability that the underdog wins the first four games is straightforward:
.45^4 = .041006 (.45 x .45 x .45 x .45)
To find the probability that the underdog wins 4 of the first 5 games, we must remember the underdog needs to win 4 of the 5 games, in any order as long as the underdog wins 4:
Start with 5 “choose” 4, to find the amount of ways the underdog may win 4 games out of 5, which is 5. Next, multiply 5 by the (0.45^4 * 0.55^1) (where the underdog wins 4 and the favorite wins 1). I find a probability of 0.1128.
To find the probability that the underdog wins 4 of the first 6 games, we must remember the underdog needs to win 4 of the 6 games, in any order as long as the underdog wins 4:
Start with 6 “choose” 4, to find the amount of ways the underdog may win 4 games out of 6, which is 15. Next, multiply 15 by the (0.45^4 * 0.55^2) (where the underdog wins 4 and the favorite wins 2). I find a probability of 0.1861.
To find the probability that the underdog wins 4 of the 7 games, we must remember the underdog needs to win 4 of the 7 games, in any order as long as the underdog wins 4:
Start with 7 “choose” 4, to find the amount of ways the underdog may win 4 games out of 7, which is 35. Next, multiply 35 by the (0.45^4 * 0.55^3) (where the underdog wins 4 and the favorite wins 3). I find a probability of 0.2388.
Hope you find this useful!
Minahil F.
Thank You! That was really helpful.04/06/22