Credit scorecards are used by financial institutions to help decide to whom loans should be granted (see the Applications in Banking: Credit Scorecards summary on page 63). An analysis of the records of one bank produced the following probabilities.

Score Loan Performance Under 400 400 or More Fully repaid .19 .64 Defaulted .13 .04

a. What proportion of loans are fully repaid?

b. What proportion of loans given to scorers of less than 400 fully repay?

c. What proportion of loans given to scorers of 400 or more fully repay?

d. Are score and whether the loan is fully repaid independent? Explain.