# A can hit a target 4 times in 5 shots, B can hit 3 times in 4 shots, and C can hit 2 times in 3 shots. Calculate the probability that

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A can hit a target 4 times in 5 shots, B can hit 3 times in 4 shots, and C can hit 2 times in 3 shots. Calculate the probability that

(i) A, B and C all hit the target

(ii) B and C hit and A does not hit the target.

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Given : let A , B and C chances of hitting a target is given i.e ,

P(A) = $\frac{4}{5},$ P(B) = $\frac{3}{4}$ and P(C) = $\frac{2}{3},$

To Find:

(i) The probability that A , B and C all hit the target.

Now ,P(all hitting the target) = P(A ∩ B ∩ C)

Hence , The probability that A , B and C all hit the target is$\frac{2}{5}$

(ii) B and C hit and A does not hit the target

Here, P(B and C hit and not A) = P(B ∩ C ∩ $\overline A$)

Hence , the probability that B and C hit and A does not hit the target is$\frac{1}{10}$