Question

A production lot of size 100 is known to be a% defective. A random sample of 12

items is selected without replacement. Determine the probability that there will be

no defective in the sample.

Answer 1

Let $X=$ the number of defective items in the sample: $x\sim Bin(n, p).$

Given $n=12, p=0.01a, q=1-p=1-0.01a$

$$P(X=0)=\dbinom{12}{0}(0.01a)^0(1-0.01a)^{12-0}$$

$$=(1-0.01a)^{12}$$