An automobile insurance company divides customers into three categories, good ri

Question

An automobile insurance company divides customers into three categories, good risks, medium risks, and poor risks. Assume that 70% of the customers are good risks, 20% are medium risks, and 10% are poor risks. Assume that during the course of a year, a good risk customer has probability 0.005 of filing an accident claim, a medium risk customer has probability 0.01, and a poor risk customer has probability 0.025. A customer is chosen at random. a. What is the probability that the customer is a good risk and has filed a claim? b. What is the probability that the customer has filed a claim? c. Given that the customer has filed a claim, what is the probability that the customer is a good risk?

Explanation / Answer

P(G)=0.7, P(M)=0.2, P(P)=0.1

P(claim|the G)=0.005

P(claim| M)=0.01

P(claim | P)= 0.025

A. P(G and complaint)=0.005*0.7= 0.0035

B. P( claim)= 0.005*0.7+0.01*0.2+0.025*0.1

C. P(G| claim)= 0.0035/( 0.005*0.7+0.01*0.2+0.025*0.1)

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