Solution Found!
Two athletic teams play a scries of games; the first team
Chapter 4, Problem 72P(choose chapter or problem)
Problem 72P
Two athletic teams play a scries of games; the first team to win 4 games is declared the overall winner. Suppose that one of the teams is stronger than the other and wins each game with probability .6, independently of the outcomes of the other games. Find the probability, for i = 4, 5, 6, 7, that the stronger team wins the series in exactly i games. Compare the probability that the stronger team wins with the probability that it would win a 2-out-of-3 series.
Questions & Answers
QUESTION:
Problem 72P
Two athletic teams play a scries of games; the first team to win 4 games is declared the overall winner. Suppose that one of the teams is stronger than the other and wins each game with probability .6, independently of the outcomes of the other games. Find the probability, for i = 4, 5, 6, 7, that the stronger team wins the series in exactly i games. Compare the probability that the stronger team wins with the probability that it would win a 2-out-of-3 series.
ANSWER:
Solution:
Step 1 of 2:
Here two athletic teams play a series of games.
The first team who wins 4 games independently is declared as the overall winner.
We have to find the probability that a stronger team wins the series in exactly i games.
We also want to compare the probability that the stronger team wins with the probability that it would win a 2-out- of -3 series.