Exam P Practice Problem 110 – likelihood of auto accidents
Problem 110-A
An actuary studied the likelihood of accidents in a one-year period among a large group of insured drivers. The following table gives the results.
Age Group | Percent of Drivers | Probability of 0 Accidents | Probability of 1 Accident |
---|---|---|---|
16-20 | 15% | 0.20 | 0.25 |
21-30 | 25% | 0.35 | 0.40 |
31-50 | 35% | 0.60 | 0.30 |
51-70 | 20% | 0.67 | 0.23 |
71+ | 5% | 0.50 | 0.35 |
Suppose that a randomly selected insured driver in the studied group had at least 2 accidents in the past year. Calculate the probability that the insured driver is in the age group 21-30.
Problem 110-B
An auto insurance company performed a study on the frequency of accidents of its insured drivers in a one-year period. The following table gives the results of the study.
Age Group | Percent of Drivers | Probability of At Least 1 Accident |
---|---|---|
16-20 | 10% | 0.30 |
21-40 | 20% | 0.20 |
41-65 | 35% | 0.10 |
66+ | 35% | 0.12 |
A randomly selected insured driver from the study was found to have no accidents in the one-year period.
Calculate the probability that the insured driver is from the age group 16-20.
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