3. A customer has approached PDCD Bank Corporation for a $20,000 one-year loan at 10% interest. If the bank does not approve the loan, the $20,000 will be invested in bonds that earn a 3% annual return. Without further information, the bank feels that there is a 4% chance that the customer will totally default on the loan. If the customer defaults, the bank loses $20,000. At a cost of $500, the bank can thoroughly investigate the customer's credit record and provide a favorable or unfavorable recommendation. In the past when the customer did not default, the bank correctly predicted it 80% of the time. If, however, when the customer defaulted, the bank had made a wrong prediction 25% of the time.

a) How can the bank maximize its expected profits? Solve the problem by constructing the decision tree.

b) What is the maximum amount the bank is willing to pay for thoroughly investigating the customer's credit score?