An insurance agent has 1 0 policyholders who are considered

An insurance agent has 1 0 policyholders who are considered high risk. The probability that one of these clients will file a major claim in the next year is 0.02. W hat is the probability that at most 2 clients will file major claim s in the nex t year?

Solution

Given X follows Binomial distribution with n=10 and p=0.02

P(X=x)=10Cx*(0.02^x)*(0.98^(10-x)) for x=0,1,..,10

So the probability is

P(X<=2) = P(X=0)+P(X=1)+P(X=2)

=10C0*(0.02^0)*(0.98^(10-0))+...+10C2*(0.02^2)*(0.98^(10-2))

=0.9991361