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?