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26 August, 15:16

Al and Bill each have two bullets. They fire alternately at a glass bottle. Al has hitting probability 1/3 and Bill 1/4. What is the probability that Al smashes the bottle if he is the one who fires the first shot? (Note: Al can smash the bottle even if he misses with his first shot.)

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  1. 26 August, 19:14
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    P (Al hits bottle first time) = 1/3

    P (Al misses the first shot but hits on his second shot) =

    P (Al misses and bill misses and Al hits) = 2/3 * 3/4 * 1/3 = 1/6

    So required probability = 1/3 + 1/6 = 1/2
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