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 isks Assume that 75% of the customers are good risks, 15% are medium risks, and 10% are poor risks. Assume that during the course of a year, a good risk customer has probability 0.01 of filing an accident claim, a medium risk customer has probability 0.02, and a poor risk customer has probability 0.025. A customer is chosen at random. Determine: The probability that the customer is a good risk and has filed a claim is (4DP)? b. The probability that the customer has filed a claim is (3DP)? c. Given that the customer has filed a claim, the probability that the customer is a good risk is.4DP)?

Explanation / Answer

P(good risks) = 0.75

P(medium risks) = 0.15

P(bad risks) = 0.1

P(filed a claim | good risks) = 0.01

P(filed a claim | medium risks) = 0.02

P(filed a claim | bad risks) = 0.025

B) P(filed a claim) = P(filed a claim | good risks) * P(good risk) + P(filed a claim | medium risks) * P(medium risks) + P(filed a claim | bad risks) * P(bad risks)

= 0.01 * 0.75 + 0.02 * 0.15 + 0.025 * 0.1

= 0.013

C) P(good risk | filed a claim) = P(filed a claim | goog risks) * P(good risk) / P(filed a claim)

= 0.01 * 0.75 / 0.013

= 0.5769

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