A customer approached a bank for a $50, 000 loan at 12% interest annu-ally. If thebank does not approve the loan, the bank will invest its $50, 000 to bonds with a 6%return annually. There are two types of customers, good and bad. Good customers neverdefault and bad customer will default. By past experience, the bank knows that 4% ofcustomers are bad, in which case the bank loses the entire $50, 000.Suppose the bank can cost $500 to run a credit check to get favorable or unfavorablerecommendation, such that77P(favorable rec.good customer)961P(favorable rec.|bad customer) =4(Good customers are more likely to get a good rec., but there may still be errors.)1. Suppose the bank purchases the credit check service. Should the bank follow therecommendation?2. What should the bank do to maximize expected profit? 1. Grant the loan directly.2. Reject the loan directly. 3. Pay $500 to rum credit check and decide accordingto whether a favorable recommendation is received.3. What is the bank's maximum willingness to pay for the credit check service?

1)GivenThe loan amount =$50,000Annual interest rate on loan =12%Annual returns on the bond =6% The…

Answered: A customer approached a bank for a $50,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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