Question: Suppose the New York Yankees and Philadelphia Phillies (two Major League Baseball teams) are playing a best-of-three series. The first team to win two games is the winner of the series, and the series ends as soon as one team has won two games. The first game is played in New York, the second game is in Philadelphia, and if necessary the third game is in New York. The probability that the Yankees win a game in their home park is 0.55. The probability that the Phillies win a game in their home park is 0.53. You can assume that the outcomes of the games are independent.
a. Find the probability that the Yankees win the series.
b. Suppose you are a Yankees fan, so you place a bet on each game played where you win $100 if the Yankees win the game and you lose $105 if the Yankees lose the game. Find the distribution of your net winnings. Then find the mean and standard deviation of this distribution. Is this betting strategy favorable to you?
c. Repeat part a, but assume that the games are played in Philadelphia, then New York, then Philadelphia. How much does this "home field advantage" help the Phillies?
d. Repeat part a, but now assume that the series is a best-of-five series, where the first team that wins three games wins the series. Assume that games alternate between New York and Philadelphia, with the first game in New York.