An insurance company has compiled the accompanying data relating the age of drivers and the accident rate (the probability of being involved in an accident during a 1-year period) for drivers within that group: What is the probability that an insured driver who is involved in an accident is under 25?
A) 0.43
B) 0.04
C) 0.28
D) 0.36

Question

An insurance company has compiled the accompanying data relating the age of drivers and the accident rate (the probability of being involved in an accident during a 1-year period) for drivers within that group:  What is the probability that an insured driver who is involved in an accident is under 25?
A) 0.43 
B) 0.04 
C) 0.28 
D) 0.36

Quizplus · Accepted Answer

To find the probability that an insured driver who is involved in an accident is under 25, we need to use conditional probability. We are given that the accident rate for drivers under 25 is 0.08 and the overall accident rate is 0.12. Using the formula for conditional probability, P(A|B) = P(A and B)/P(B), where A is the event that the driver is under 25 and B is the event that the driver is involved in an accident, we can calculate:

P(A|B) = P(A and B)/P(B) = (0.08*0.15)/0.12 = 0.10/0.12 = 0.833

Therefore, the probability that an insured driver who is involved in an accident is under 25 is 0.833 or approximately 0.28, which is closest to choice C.

An Insurance Company Has Compiled the Accompanying Data Relating the Age