Answer to Question #186470 in Statistics and Probability for hassaan

Question

Q. Lots of 40 components each are called unacceptable if they contain as many as 3 defectives or more. The procedure for sampling the lot is to select 5 components at random and to reject the lot if a defective is found. What is the probability that exactly 1 defective is found in the sample if there are 3 defectives in the entire lot?

Answer 1

Let X be the number of defective items.

Then using the hypergeometric distribution with $n=5,N=40 \text{ and } k=3$

X~HG(40,5,3)

$P(X=1)=\dfrac{^3C_1\times ^{40-3}C_{5-1}}{^{40}C_5}=\dfrac{^3C_1\times ^{37}C_4}{^{40}C_5}=0.3011$