Question

A sample of 4 different calculators is randomly selected from a group containing 18 that are defective and 35 that have no defects. What is the probability that at least one of the calculators is defective?

Answer 1

Given X~Binomial(n=4, p=18/(18+35)=0.34)
P(X=x)=xC4*(0.34^x)*((1-0.34)^(4-x))

So the probability is
P(X>=1)=1-P(X=0)=1-0C4*(0.34^0)*((1-0.34)^(4-0))
=1-(1-0.34)^4
= 0.8102526