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:

Atleast 2 out of the 10 randomly selected policies will be 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 $n=10, p=0.2,q=0.8$

$$P(X\ge2)=1-P(X=0)-P(X=1)$$

$$=1-\dbinom{10}{0}(0.2)^0(0.8)^{10-0}-\dbinom{10}{1}(0.2)^1(0.8)^{10-1}$$

$$=1-0.1073741824-0.268435456$$

$$=0.6241903616$$