Solved: An automobile insurance company divides customers into three categories, good

Chapter 2, Problem 20

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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?

Equation Transcription:

Text Transcription:

70%

20%

10%

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