Question

A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is

1. 0.0036 
2. 0.1937
3. 0.2234
4. 0.3874 

Answer 1

Correct Answer - Option 2 : 0.1937

Concept:

The probability that exactly 2 of the chosen items are defective is given as,

By Binomial distribution,

\(P(x=2)\;=\;{}_{}^n{C_x}~{(p)^x}~{q^{(n - x)}}\)

where, p = probability of success, q = probability of failure

Calculation:

Given:

n = 10, x = 2, p = 0.1, q = 0.9

Therefore, P(exactly 2 of the chosen items are defective) = ¹⁰C₂ × 0.1² × 0.9^{10 - 2} ⇒ 45 × 0.01 × 0.43 = 0.1937