A customer has approached a bank for $100,000 1-year loan at 12% interest rate. If the bank does not approve this loan application, the $100,000 will be invested in bonds that earn a 6% annual return. Without additional information, the bank believes that there is a 4% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the bank will lose $100,000. At the cost of $1,000, the bank can thoroughly investigate the customer's credit record and supply a favorable or unfavorable recommendation. Experience indicates that in cases where the customer did not default on the approved loan, the probability of receiving a favorable recommendation on the basis of the credit investigation was 80%. Furthermore, in cases where the customer defaulted on the approved loan, the probability of receiving a favorable recom- mendation on the basis of the credit investigation was 20%. Suppose there is 77.6% to get a favorable result. Draw the decision tree using DADM Tools and answer the following questions. Round your probability calculations up to 3 decimal places. (a) (Bayes) What is the posterior probability that the customer with a favorable recommen- dation won't default? (b) What is the EM of the bank's optimal course of action? (c) What is the Expected Value of Sample Information (EVSI)? (d) What is the Expected Value of Perfect Information (EVPI)? (e) How much increase of the investigation cost would make the bank indifferent to whether to investigate or not