An insurance company found that 2.5%of male drivers between theages of 18 and
25 are involved in serious accidents annually. Assume that every such accident costs the company $65,000 and that a driver can only have one of these accidents in ayear.
(a) If the company charges $2,500 forsuch coverage, what is the probability 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 theprobability that thecompany makes a profit on these policies? Assume that the drivers don't run into each other and behave independently.
(c) Does the difference between the probabilities of parts (a) and (b)explain how insurance companies stayin business? Large auto insurers are certainly profitable. One report, for example, claims that Allstate pays out less than $0.50 in accident claims for every dollar collected in premiums.