John has a choice between two options, to play 3 tennis sets with his father ("F") and Bill ("B"), a tennis champion. He can either play in the order F-B-F, or in the order B-F-B. Bill is a better player than his father. If John wins two sets in a row, he will win a prize.
(a) Which order should John choose? Why?
(b) Let Z be the number of times John wins. If, instead, John wanted to maximize E[Z], should he make a different choice? Why or why not?