Question

A shipment of 60 parts contains 9 defective parts. Suppose 3 parts are selected at random, without replacement, from the shipment. What is the probability that at most one part is not defective?

Options:

	0.9439
	0.0887
	0.0561
	0.0296

Answer 1

A shipment of 60 parts contains 9 defective parts and

60 - 9 = 51 non-defective parts.

Suppose 3 parts are selected at random, we want to find, the probability that at most one part is not defective.

Let X be a non-defective parts among 3 parts.

We can select 3 parts from 60 by following number of ways: ⁶⁰C₃ = 34220

We want to find, P(X <= 1)

P(X <= 1) = P(X = 0) + P(X = 1)

here, (X = 0) means, we select all 3 defective parts by following number of ways,

⁵¹C₀ * ⁹C₃ = 1 * 84 = 84

and (X = 1) means, we select 1 non-defective part and 2 defective parts by,

⁵¹C₁ * ⁹C₂ = 51 * 36 = 1836

Therefore,

P(X = 0) = 84/34220

P(X = 1) = 1836/34220

=> P(X <= 1) = (84/34220) + (1836/34220) = 1920/34220

=> P(X <= 1) = 0.0561

Hence, required probability is 0.0561