PROBLEM 4E

Assume that an insurance company knows the following probabilities relating to automobile accidents (where the second column refers to the probability that the policyholder has at least one accident during the annual policy period):

A randomly selected driver from the company’s insured drivers has an accident. What is the conditional probability that the driver is in the 16–25 age group?

Step 1:

The probabilities relating to automobile accidents is given by an insurance company.

Age of drivers |
Probabilities of accidents |
Fraction of company’s insured drivers. |

16-15 |
0.05 |
0.10 |

26-50 |
0.02 |
0.55 |

51-65 |
0.03 |
0.20 |

66-90 |
0.04 |
0.15 |

If a randomly selected driver from the company’s insured drivers has an accident. We have to find the conditional probability that the driver is in the 16–25 age group.