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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\(\frac{1}{10}\)

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