A mortgage lender attempted to increase its business by marketing its subprime mortgage. This mortgage is designed for people with a less than perfect credit rating, then the interest rate is higher to offset the extra risk. In the past year, 20% of these mortgages resulted in foreclosure as customers defaulted on their loans. A new screening system has been developed to determine whether to approve customers for the subprime loans. When the system is applied to a credit application, the system will classify the application as " Approve for loan" or " Reject for loan". When this new system was applied to recent customers who had defaulted on their loans, 90% of these customer were classified as " reject". When this same system was applied to recent loan customers who had not defaulted on their loan payments, 70% of these customer were classified as " approve"

a- If a customer did not default on a loan, what is the probability that the rating system would have classified the applicant in the reject category?

b- If the rating system had classified the applicant in the reject category, what is the probability that the customer would not default on a loan?