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. 

Answer 1

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`