An insurance company believes that people can be divided int

An insurance company believes that people can be divided into two classes – those that are accident-prone and those that are not. Their statistics show that an accident-prone person will have an accident within a fixed 1-year period with probability 0.4, whereas this probability decreases to 0.2 for a non accident-prone individual.

a) If we assume that 30 percent of the population is accident prone, what is the probability that a new policyholder will have an accident within a year of purchasing a policy?

b) Suppose that a new policyholder has an accident within a year of purchasing his policy. What is the probability that he is accident-prone?

Solution

a) 30% are accident prome = 0.30

70% are not accident prone = 0.70

accident prone met with accident = 0.4

hence he will met accident = 0.4*0.30 = 0.12

non accident prone met with accident = 0.2

hence he will met with accident = 0.70*0.2= 0.14

hence the total probability = 0.12+0.14 = 0.26

b) as in avove part shown that accident prone met with accident = 0.12

total chance of accident prone = 0.30

probability that he will be accident prone = 0.12/0.30 = 0.4