61. Suppose in Exercise 29 that the shooting ends when the target has been hit twice.

Letmi denote the mean number of shots needed for the first hit when player i shoots first, i = 1, 2. Also, let Pi , i = 1, 2, denote the probability that the first hit is by player 1, when player i shoots first.

(a) Find m1 and m2.

(b) Find P1 and P2.

For the remainder of the problem, assume that player 1 shoots first.

(c) Find the probability that the final hit was by 1.

(d) Find the probability that both hits were by 1.

(e) Find the probability that both hits were by 2.

(f) Find the mean number of shots taken.