Question

Suppose a population consists of 10 items, four of which are classified as defective and six of which are classified as non-defective. What is the probability that a random sample of size three will contain two defective items?

Answer 1

N=10

n=3

x=2

k=4

Hypergeometric distribution

$P(X) = \frac{\binom{k}{x} \binom{N-k}{n-x}}{\binom{N}{n}} \\ P(2) = \frac{\binom{4}{2} \binom{10-4}{3-2}}{\binom{10}{3}} \\ P(2) = \frac{6 \times 6}{120} = 0.3 \\ P(2) = 0.3$