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, and 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 customers 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 customers were classified as "Approve for loan."
(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?