Question

Solve the following problem :

The probability that a component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 components tested 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)
= `""^4"C"_2 (0.6)^2 (0.4)^(2)`
= 6(0.36) (0.16)
= 0.3456