An automobile insurance company is in the process of reviewing its policies.Currently,drivers under the age of 25 have to pay a premium.The company is considering increasing the premium charged to drivers under 25.According to company records,35 percent of the insured drivers are under the age of 25.The company records also show that 280 of the 700 insured drivers under the age of 25 have been involved in at least one automobile accident.On the other hand,only 130 of the 1300 insured drivers 25 years or older have been involved in at least one automobile accident.
An accident has just been reported.What is the probability that the insured driver is under the age of 25?
A)35%
B)20.5%
C)14%
D)68.3%
E)40%

Question

Quizplus · Accepted Answer

The probability that the insured driver is under the age of 25 given an accident has occurred is calculated using Bayes' theorem. The probability is (280/410) = 68.3%, where 410 is the total number of accidents (280 under 25 + 130 over 25).

An Automobile Insurance Company Is in the Process of Reviewing