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Suppose that an insurance company classifies people into
Chapter 3, Problem 50P(choose chapter or problem)
Problem 50P
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, .15, and .30. 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? If policyholder A had no accidents in 2012, what is the probability that he or she is a good risk? is an average risk?
Questions & Answers
QUESTION:
Problem 50P
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, .15, and .30. 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? If policyholder A had no accidents in 2012, what is the probability that he or she is a good risk? is an average risk?
ANSWER:
Step 1 of 2
From the given problem we have The proportion of people:
Good risk = 20%,
Average risk = 50%, and
Bad risk = 30%.
The probabilities of accidents:
P(good risk) = 0.05,
P(average risk) = 0.15, and
P(bad risk) = 0.30.
We need to find the probability that he or she is a good risk. And also we have to find the probability that he or she is an average risk.