Suppose the Boston Red Sox and the New York Yankees (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 Boston, the second game is played in New York, and if necessary the third game is in Boston. The probability that the Red Sox win a game in Boston is 0.55. The probability that the Yankees win a game in New York is 0.53. Assume the outcomes of the games are independent. a. Use PrecisionTree to contruct a probability tree to represent this problem.
b. What is the probability the Red Sox win the series, i. e., they win two games?
c. Suppose you are a Red sox fan, so you place a bet on each game played where you win $100 if the Red Sox win the game and you lose $105 if the Red Sox lose the game. Find the distribution of your net winnings. Then find the expected net winnings?