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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.

      \displaystyle \bold ( \bold A \bold ) \ \ \ \ \ \ \ \ \ \ \ \  \bold 0 \bold . \bold 1 \bold 7

      \displaystyle \bold ( \bold B \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 2 \bold 4

      \displaystyle \bold ( \bold C \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 3 \bold 0

      \displaystyle \bold ( \bold D \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 4 \bold 0

      \displaystyle \bold ( \bold E \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 4 \bold 5

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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.

      \displaystyle \bold ( \bold A \bold ) \ \ \ \ \ \ \ \ \ \ \ \  \bold 0 \bold . \bold 0 \bold 8

      \displaystyle \bold ( \bold B \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 1 \bold 2

      \displaystyle \bold ( \bold C \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 1 \bold 5

      \displaystyle \bold ( \bold D \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 1 \bold 9

      \displaystyle \bold ( \bold E \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 2 \bold 0

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Answers

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probability exam P

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