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 value of the premium charged to drivers under 25.According to company records,35% 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 had been involved in at least one automobile accident.On the other hand,only 130 of the 1300 insured drivers 25 years or older had 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 is 68.3%. This is because there are 700 insured drivers under the age of 25 and 1300 insured drivers 25 years or older, so the total number of insured drivers is 2000. Of the 2000 insured drivers, 280 have been involved in at least one automobile accident, so the probability that an insured driver has been involved in at least one automobile accident is 280/2000 = 0.14. The probability that an insured driver is under the age of 25 and has been involved in at least one automobile accident is 280/2000 * 700/2000 = 0.0683. The probability that an insured driver is under the age of 25 given that they have been involved in at least one automobile accident is 0.0683/0.14 = 0.683, or 68.3%.

An Automobile Insurance Company Is in the Process of Reviewing