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2. Anauto insurance company charges younger drivers a higher premiumthan it does

ID: 2916010 • Letter: 2

Question

2.      Anauto insurance company charges younger drivers a higher premiumthan it does older drivers because younger drivers as a group tendto have more accidents. The company has 3 age groups: Group Aincludes those under 25 years old, 22% of all itspolicyholders. Group B includes those 25-39 years old, 43% ofall its policyholders, Group C includes those 40 years old andolder. Company records show that in any given one-yearperiod, 11% of its Group A policyholders have an accident. The percentages for groups B and C are 3% and 2%, respectively.

a)   What percent of thecompany’s policyholders are expected to have an accidentduring the next 12 months?

b)   Suppose Mr. X has justhad a car accident. If he is one of the company’spolicyholders, what is the probability that he is under 25?

Explanation / Answer

Group A (under 25 years)--> 22% policyholders43 % policyholders=40 years)--> 35% policyholders