You are playing Serena Williams in tennis, and you have a 42% chance of winning each point.
a. Use simulation to estimate the probability you will win a particular game. Note that the first player to score at least four points and have at least two more points than his or her opponent wins the game.
b. Use simulation to determine your probability of winning a set. Assume that the first player to win six games wins the set if he or she is at least two games ahead; otherwise, the first player to win seven games wins the set. (We substitute a single game for the usual tiebreaker.)
c. Use simulation to determine your probability of winning a match. Assume that the first player to win three sets wins the match.
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