Anthony and Bryan are playing a baseball batting contest. The rules are each of them will try to hit a baseball. If one hits and the other misses, then the one hit the ball is declared the winner. If both of them hit or both of them miss, then they repeat the process. Suppose that the results of the at bats are independent and Anthony will hit the ball with probability pA, and Bryan will hit the ball with probability pB. What is

(a) the probability that Anthony is the winner of the contest?

(b) the probability that the contest ends after the nth round of batting?

(c) the conditional probability that the contest ends after the nth round of batting given that A is the winner?