The World Series of baseball is to be played by team A and team B. The first team to win four games wins the series. Suppose that team A is the better team, in the sense that the probability is 0.6 that team A will win any specific game. Assume also that the result of any game is independent of that of any other.
a. What is the probability that team A will win the series?
b. What is the probability that a seventh game will be needed to determine the winner?
c. Suppose that, in fact, each team wins two of the first four games.
i What is the probability that team A will win the series?
ii What is the probability that a seventh game will be needed to determine the winner?