Question

The probability of hitting a target in any shot is 0.2. If 5 shots are fired, find the probability that the target will be hit at least twice.

Answer 1

Here n = 5

P(success) = P(target will be hit) = 0.2

∴ p = 0.2,

q = 1 – 0.2 = 0 .8

Let X = Number of times the target is hit.

Then X ∼ B (n = 5, p = 0.2)

Then p.m.f. of X is given by

P(X = x) = P(x)

= ⁵C_x (0.2)^x (0.8)^{5 – x}, x = 0, 1, 2, ... 5

∴ P(target is hit at least twice out of 5 shots)

= 1 – [P(0) + P(1)]

= 1 – [⁵C₀ (0.2)⁰ (0.8)⁵ + ⁵C₁ (0.2)¹ (0.8)⁴]

= 1 – [(1) (1) (0.328) + (5) (0.2) (0.4096)]

= 1 – [0.328 + 0.4096]

= 1 – 0.7376

= 0.2624