This problem is tricky, but amusing. Three gunmen, A, B and C, are shooting at each other. The probabilities that each will hit what they aim at are respectively 1, 0.75, 0.5. They take it in turns to shoot (in alphabetical order) and continue until only one is left alive. Calculate the probabilities of each winning the contest. (Assume they draw lots for the right to shoot first.)

1: Start with one-on-one gunfights, e.g. the probability of A beating B, or of B beating C.

2: You’ll need the formula for the sum of an infinite series, given in Chapter 1.