Question

#10) 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 0.00s of filing an accident claim a medium risk customer has probability 0.01 and a poor risk customer has probability 0.02s chosen at random. [Let GR denote good risks, MR denote medium risks, PR denote poor m er is enote file an accident claim.] a) What is the probability that the customer is a good risk and has fied 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?

Answer 1

here accident claim term is not clear I assume it is AC

a)probability =P(GR and filed a claim)= P(GR)*P(AC|GR) =0.7*0.005=0.0035

b)P(AC) = P(GR)*P(AC|GR)+ P(MR)*P(AC|MR)+ P(PR)*P(AC|PR)

=0.7*0.005+0.2*0.01+0.1*0.025=0.008

c) P(GR|AC) = P(GR)*P(AC|GR)/P(AC) =0.7*0.005/0.008=0.4375