Ideally, auto insurance rates are lower for good drivers than for bad drivers, but an insurer needs to be able to tell which type of driver a client is. Assume that all drivers are considered as either “good drivers” or “bad drivers” and that the probability of a random driver being a “good driver” is 0.80. In addition, suppose that the probability of 2 accidents in a year is 0.02 for good drivers and 0.10 for bad drivers.

(a) If an insurer has no additional information about an applicant’s driving history, what is the probability that the individual is a bad driver?

(b) If the insurer knows that the applicant had 2 accidents in the past year, what is the probability that he or she is a bad driver?