Quality control: prob. sample contains exactly 2 defectives

[Guest]

A manufacturer produces electrical switches, of which 2% are defective. From a production run of 50,000 switches, four are randomly selected and each is tested. Determine the probability that the sample contains exactly two defective switches. Round your answer to three decimal places. Assume that the four trials are independent and that the number of defective switches in the sample has a binomial distribution.

 

[galactus]

You could use a hypergeometric distribution.

\(\displaystyle \L\\\frac{C(k,x)C(N-k,n-x)}{C(N,n)}\)

N=population size
k=successes
N-k=failures
n=sample size
x=successes in sample
n-x=failures in sample