# 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. - Mathematics and Statistics

Sum

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.

#### Solution

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

Is there an error in this question or solution?

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Part II | Q 1.07 | Page 157