Question

Global insurance has found that 20% (1 in 5) of all insurance policies are surrendered (cashed in) before their maturity date. Assume that 10 policies are randomly selected from the policies data base

What is the probability that:

4 of the 10 insurance policies will have been surrendered before their maturity date?

Answer 1

Let $X=$ the numbers of insurance policies surrendered (cashed in) before their maturity date: $X\sim Bin (n, p).$

Given $n=10, p=0.2,q=0.8$

$$P(X=4)=\dbinom{10}{4}(0.2)^4(0.8)^{10-4}=0.088080384$$