In the women’s tennis finals at Wimbledon, the match winner is the first player to win two sets. Sets continue one after the other until there is a winner and loser; there are no ties. If one woman wins the first two sets, the match is finished at two sets. The maximum possible number of sets in a match is three.

a. Imagine that two women are equal in ability, so the probability of each woman winning any single set is 0.50. Use a probability tree to find the probability that a match lasts exactly two sets. What is the probability that the match lasts exactly three sets?

b. Imagine that one woman was better than the other, such that the probability of her victory in any set is 0.55. Use a probability tree to find the probability that the weaker player would win the match.