Question

An insurer has 5 independent one-year term life insurance policies. The face amount on each policy is 100,000. The probability of a claim occurring in the year for any given policy is 0.2. Find the probability the insurer will have to pay more than the total expected claim for the year.

Answer 1

here expected claim of 5 policies =5*100000*0.2 =100000

probability the insurer will have to pay more than the total expected claim for the year

=P(2 or more claim in the year)

-=P(X>=2)=1-P(X<=1) =1-(5C0)*(0.2)^0*(0.8)^5-(5C1)*(0.2)^1*(0.8)^4

=1-0.3277-0.4096

=0.2627