Problem: Suppose that in a group of insurance policies (which are independent as regards occurrence of claims), 20% of the policies have incurred claims during the last year. An auditor is examining the policies in the group one by one in random order until two policies with claims are found.

Required:

(i) Determine the probability that exactly five policies have to be examined until two policies with claims aren found.

(ii) Find the expected number of policies that have to be examined until two policies with claims are found.