Question

An insurance company found that 25% of all insurance policies are terminated before their maturity date. Assume that 10 policies are randomly selected from the company's policy database. Assume a binomial experiment.

What is the probability that at most 8 policies and not terminated before maturity?

Answer 1

$p=0.25,q=1-p=1-0.25=0.75 ,n=10$

Let X be the number of policies terminated before maturity-

 Probability that at most 8 policies and not terminated before maturity-

$P(X\le 8)=1-P(X>8)=1-[P(X=9)+P(X=10)]$

$=1-[^{10}C_9(0.25)^9(0.75)^1+^{10}C_{10} (0.25)^{10}]\\[9pt]=1-(0.0000286+0.000009536)\\[9pt]=1-0.00002955=0.999997$