A local bank is reviewing its credit-card policy with a view toward recalling some of its credit cards. In the past, approximately 5% of cardholders have defaulted and the bank has been unable to collect the outstanding balance. Hence, management has established a prior probability of 0.05 that any particular cardholder will default. The bank has further found probability of missing one or more monthly payments is 20% for customers who do not default. Of course, the probability of missing one or more payments for those who default is 100%. a. Given that a customer has missed a monthly payment, what is the posterior probability that the customer will default? (Show your work by following the steps as you did in questions “a” to “c” in Question #1 above.) b. The bank would like to recall its card if the probability that a customer will default is greater than 20%. Should the bank recall its card if the customer misses a monthly payment? Why or why not? c. The current economic climate has been improving and the company has recently implement some new collection policies. The bank now feels that the percentage of customers defaulting is much better and is estimated to be 3.75%. Given the 20% ceiling criteria for defaulting as stated in question b, what is the revised posterior probability? Should the bank recall its card if the customer misses a monthly payment? Why or why not?