1.A mortgage lender is trying to increase its business by marketing its subprime mortgage. This mortgage is designed for people with less than perfect credit rating, and the interest rate is higher to offset the extra risk. In the past year, 15% of these mortgages resulted in foreclosure as customers defaulted on their loans.A new screening system has been developed to determine whether to approve the 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, 95% 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, 75% of these customers were classified as 'approve for loan'.

aIf the rating system has classified an applicant in the 'approve for loan' category, what is the probability that the customer would default on a loan? Show your work.

b.What is the probability that the rating system may classify an applicant in 'approve for loan' category? Show your work.

c.If the rating system has classified an applicant in the 'reject' category, what is the probability that the customer would not default on a loan? Show your work.