Assume the New York Yankees and Boston Red Sox (two Major League Baseball teams) are playing the best-of-three series. The first team to win two games is the winner of series, and series ends as soon as one team has won two games. The first game is played in New York, the second game is played in Boston, and if necessary the third game is in New York. The probability that the Yankees win a game in New York is 0.55. The probability that the Red Sox win a game in Boston is 0.53. Assume the outcomes of the games are independent.
a) What is the probability the Yankees win the series, i.e., they win two games?
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 expected net winnings?