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Suppose the New York Yankees and Philadelphia Phillies 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 0.65 and the probability that the Phillies win a game in their home park is 0.60. You can assume that the outcomes of the games are independent for the parts a and b.
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 $200 if the Yankees win the game and you lose $210 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. Now suppose that each team's probability of winning increases by 10% if they win the first match. Using the new information, find the probability that the Yankees win the first two matches.
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