Eagle Credit Union (ECU) has experienced a 10% default rate with its commercial loan customers (i.e., 90% of commercial loan customers pay back their loans). ECU has developed a statistical test to assist in predicting which commercial loan customers will default. The test assigns either a rating of “Approve” or “Reject” to each loan applicant. When applied to recent commercial loan customers who paid their loans, the test gave an “Approve” rating in 80% of the cases examined. When applied to recent commercial loan customers who defaulted, it gave a “Reject” rating in 70% of the cases examined.

a. Use this data to construct a joint probability table.

b. What is the conditional probability of a “Reject” rating given that the customer defaulted?

c. What is the conditional probability of an “Approve” rating given that the customer defaulted?

d. Suppose a new customer receives a “Reject” rating. If that customer gets the loan anyway, what is the probability of default?