Question

A production process produces 2% defective parts. a sample of five parts from the production process is selected. what is the probability that the sample contains exactly two defective parts?

Answer 1

.0038



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Answer 2

We have:

p=0.02
n=5
k=2

$P(success ~2)=_nC_k~*~(p)^k~*~(1-p)^{n-k}\\~\\~\\P(success ~2)=5C2~*~0.02^2*0.98^3=0.003765$

SO that the probability that the sample contains exactly two defective parts would be 0.38%