In sports, championships are often decided by two teams playing in a championship series. Often the fans of the losing team claim they were unlucky and their team is actually the better team. Suppose Team A is the better team, and the probability it will defeat Team B in any one game is 0.6.
a. What is the probability that the better team, Team A, will win the series if it is a one-game series?
b. What is the probability that the better team, Team A, will win the series if it is a best out of three series?
c. What is the probability that the better team, Team A, will win the series if it is a best out of seven series?
d. Suppose the probability that A would beat B in any given game were actually 0.7. Recompute parts a–c.
e. Suppose the probability that A would beat B in any given game were actually 0.9. Recompute parts a–c.
f. What is the relationship between the “best” team winning and the number of games played? The best team winning and the probabilities that each will win?