Suppose that an insurance company classifies people into one of
three classes: good risks, average risks, and bad risks. The
company’s records indicate that the probabilities that good-,
average-, and bad-risk persons will be involved in an accident over
a 1-year span are, respectively, .05, .10, and .25.
Q1. If 20 percent of the population is a good risk, 50
percent an average risk, and 30 percent a bad risk, what proportion
of people have accidents in a fixed year?
Q2. If policyholder A had no accidents in the previous
year, what is the probability that he or she is a good or average
risk?