When applying for insurance, potential customers are asked if they have good or

Question

When applying for insurance, potential customers are asked if they have good or bad credit. Just before approving the new customer, the insurance company orders a credit report to verify the customer's actual credit rating. Historically, 33% of customers with bad credit claim they have good credit and 26% of customers with good credit misreport they have bad credit. If the insurance company has set its credit standards so that 56% of approved customers have good credit, what is the probability an approved customer has good credit, given that they claimed to have good credit during the application process?

Explanation / Answer

probabilty that a customer claim to have good credit =(1-0.26)*0.56+(1-0.56)*0.33=0.5596

hence probability an approved customer has good credit, given that they claimed to have good credit during the application process =(1-0.26)*0.56/0.5596=0.740529

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