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The probability that a bomb hits the target is 1/4 Five bombs are aimed at the target. Find the probability that: (i) 3 bombs hit the target (ii) at the most two bombs hit the target. |
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Answer» Let x denote the number of bombs hit the target is a Binomial variate with the parameters n = 5, P = 1/4 = 0.25 and q= 1 – p= 1 – 0.25 = 0:75. The p.m.f is:- p(x) = ncx px qn-x : x = 0,1,2 n p(x)= 5cx (0.25)x (0.75)5-x x = 0,1,2……..5 (i) p(3 bombs hit the target) =p(x = 3) = 5c3 (0.25)3 (0.75)5-3 = 10 × 0.015625 × 0.5625 = 0.08789. (ii) p(at most two bombs hit the target) = p(x ≤ 2) = p(x = 0) + p[x = 1) + p(x = 2) = 5c0 (0.25)° x (0.75)5-0 + 5c1 (0.25)1 (0.75)5-1 + 5c2 (0.25)2 (0.75)5-2 = 1 × 1 × 0.2373 + 5 × 0.25 × 0.3164 + 10 × 0.0625 × 0.4218 = 0.2373 + 0.3955 + 0.2637 = 0.8965. |
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