60. Two players alternate flipping a coin that comes up heads with probability p. The first one to obtain a head is declared the winner. We are interested in the probability that the first player to flip is the winner. Before determining this probability, which we will call f (p), answer the following questions.

(a) Do you think that f (p) is a monotone function of p? If so, is it increasing or decreasing?

(b) What do you think is the value of limp→1 f (p)?

(c) What do you think is the value of limp→0 f (p)?

(d) Find f (p).