Shooters a, b, and c are having a truel. the probability that shooter a hits his target is p a , the probability that b hits his target is p b and p a < p b < 1, and the probability that c hits his target is 1. they take turns, a first, then b, then c, and repeating until only one shooter is left. if a decides to shoot at c on his first turn, what is the probability that a wins? (make reasonable assumptions about the behavior of b and c.)