An insurance company believes that people can be divided into two classes: those who are accident-prone...

An insurance company believes that people can be divided into two classes: those who are accident-prone and those who are not. Their statistics show that an accident-prone person will have an accident at some time within a fixed one-year period with probability 0.4, whereas this probability decreases to 0.2 for a non-accident-pron person Assume that 30% of the population is accident-prone.

a) 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 a policy What is the probability that he or she is accident-prone?

c) What is the conditional probability that a new policyholder will have an accident in his or her second year of policy ownership, given that the policyholder had an accident in the first year?

Expert Solution

a)

probability that a new policyholder will have an accident within a year of purchasing a policy

=P(accident prone and accident)+P(not accident prone and accident)

=0.3*0.4+0.7*0.2=0.26

b)

P(accident prone given accident)=0.3*0.4/0.26=0.4615

c)

P(accident| accident in 1st year )=0.4615*0.4+(1-0.4615)*0.2 =0.2923

orchestra answered 2 years ago

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