Suppose in Exercise 25 that the shooting ends when the target has been hit twice. Let m, denote the mean number of shots needed for the first hit when player i shoots first, i = 1, 2.

Also, let P, i = 1, 2, denote the probability that the first hit is by player 1, when player i shoots first.

(a) Find m and m.

(b) Find P 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 b1.

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

(f) Find the mean number of shots taken.