An insurance company found that 2.5% of male drivers between the ages of 18 and 25 are involved in serious accidents annually. To simplify the analysis, assume that every such accident costs the insurance company +65,000 and that a driver can only have one of these accidents in a year.
(a) If the company charges +2,500 for such coverage, what is the chance that it loses money on a single policy?
(b) Suppose that the company writes 1,000 such policies to a collection of drivers. What is the probability that the company loses money?