Answer to Question #255540 in Statistics and Probability for talie

Question #255540
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?
1
Expert's answer
2021-11-16T18:54:29-0500

N=10

n=3

x=2

k=4

Hypergeometric distribution

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

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