An auto insurance compnay classifies its customers as good,bad, or average risks

Question

An auto insurance compnay classifies its customers as good,bad, or average risks. 30% are deemed good risks, 20% are deemedbad risks, and 50% are deemed average riks. Historical data suggestthat 5% of the good risks, 40% of the bad risks, and 10% of theaverage risks will be involved in a crash in the coming year. Given that a crash has occurred, what is the probability thatthe customer who crashed was classified as a good risk? Hint: G = customer is classified as good risk B = customer is classified as bad risk A = customer is classified as average risk C = customer is involved in a crash in the comingyear An auto insurance compnay classifies its customers as good,bad, or average risks. 30% are deemed good risks, 20% are deemedbad risks, and 50% are deemed average riks. Historical data suggestthat 5% of the good risks, 40% of the bad risks, and 10% of theaverage risks will be involved in a crash in the coming year. Given that a crash has occurred, what is the probability thatthe customer who crashed was classified as a good risk? Hint: G = customer is classified as good risk B = customer is classified as bad risk A = customer is classified as average risk C = customer is involved in a crash in the comingyear

Explanation / Answer

So we have 30% Good 20% Bad 50% average If 5% of good will be involved in a crash, that's 5% * 30% oftotal customers. = 0.015 If 40% of bad will be involved in a crash, that's 40% *20% of total customers. = .08 If 40% of bad will be involved in a crash, that's 40% *20% of total customers. = .08 If 10% of average will be involved in a crash, that's 10%* 50% of total customers. = .05 .015 + .08 + .05 = .145 of customers who will be involved in acrash. .015/.145 = .103448 .103448 Probability that customer who crashed was classifiedas a good risk

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