Question

The probability that certain kind of component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 tested components survive

Answer 1

Let X denote the number of tested components survive.

P(component survive the check test) = p = 0.6   ....[Given]

∴ q = 1 – p

= 1 − 0.6

= 0.4

Given, n = 4

∴ X ~ B (4, 0.6)

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

P(X = x) = `""^4"C"_x (0.6)^x (0.4)^(4 - x), x = 0, 1, ..., 4`

∴ P(exactly 2 components tested survive)

= P(X = 2)

= ⁴C₂ (0.6)² (0.4)²

= 6(0.36)(0.16)

= 0.3456