A can hit a target 5 times in 6 shots, B can hit 4 times in 5 shots and C can hit 3 times in 4 shots. What is the probability that A and C may hit but B may lose?

Explanation

The probability that A hits is P(A) = \frac{5}{6}. The probability that B hits is \frac{4}{5}, so B misses is P(B') = 1 - \frac{4}{5} = \frac{1}{5}. The probability that C hits is P(C) = \frac{3}{4}. The combined probability is P(A) \times P(B') \times P(C) = \frac{5}{6} \times \frac{1}{5} \times \frac{3}{4} = \frac{15}{120} = \frac{1}{8}.

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