Chapter 5, Problem 11P

A local bank reviewed its credit-card policy with the intention of recalling some of its credit cards. In the past, approximately 5% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a prior probability of 0.05 that any particular cardholder will default. The bank also found that the probability of missing a monthly payment is 0.20 for customers who do not default. Of course, the probability of missing a monthly payment for those who default is 1.

1. a. Given that a customer missed a monthly payment, compute the posterior probability that the customer will default.
2. b. The bank would like to recall its credit card if the probability that a customer will default is greater than 0.20. Should the bank recall its credit card if the customer misses a monthly payment? Why or why not?