Question

Suppose that 4% of all TVs made by A&B Company in 2000 are defective. If eight of these TVs are randomly selected from across the country and tested, what is the probability that exactly three of them are defective? Assume that each TV is made independently of the others.

Answer 1

Let $X=$ the number of defective selected TVs: $X\sim Bin(n, p).$

Given $n=8, p=0.04, q=1-p=0.96$

$$P(X=3)=\dbinom{8}{3}(0.04)^{3}(0.96)^{8-3}$$

$$\approx0.00292229575$$