Probability duel

Three men - conveniently named A, B, C - are fighting a duel with pistols. It's A's turn to shoot.

The rules of this duel are rather peculiar: the duelists do not all shoot simultaneously, but take turns. A fires at B, B fires at C, and C fires at A; the cycle repeats until there is a single survivor. If you hit your target, you'll fire the next person on your next turn.

For example, A might shoot and hit B. With B out of the picture, it would be C's turn to shoot - suppose he misses. Now it's A's turn again, and he fires at C; if he hits, the duel is over, with A the sole survivor.

To bring in a little probability, suppose A and C hit their target with probability 0.5, but that B is better shot, and hits with probability 0.75 - all shots are independent.

What's the probability that A wins the duel?

Probability puzzle/Getting Serious/Puzzle 11

P.S.: Sorry if there are typos! I know the answer. This is a warm-up for the next task. I won’t tell anyone if your answer is right or wrong.

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Probability duel

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