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Question
The probability that a bomb dropped from an aeroplane will strike a target is `1/5`, If four bombs are dropped, find the probability that :
(a) exactly two will strike the target,
(b) at least one will strike the target.
Solution
Let x denote the random variable that 'number of bombs strike the target'.
X ∼ B(n, p)
∴ Probability mass function is given by
P(X = x) = `""^n"C"_x . P^x . q^(n - x)`
Given ,
P = `1/5 , n = 4 , q = 1 - P = 4/5`
(a) P(x = 2) = `""^4"C"_2 xx (1/5)^2 xx (4/5)^2 = 96/625`
(b) P(at least 1) = P(x ≥ 1)
= `1 - P(x = 0)`
= `1 - ""^4"C"_0 p^0 q^4`
= `1 - 1 xx 1 xx (4/5)^4`
= `1 - 256/625`
= `369/625`
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