A bank is reviewing its credit policy with a view toward recalling some of its credit cards. It has been found 5% of cardholders have defaulted and the bank has been unable to collect the outstanding balance. The bank has also found that the probability of missing one or more payments is 0.2 for customers who do not dfault. The probability for customers who default is, of course, 1. Should the bank recall its card if the probability that a customer will defualt is greater than 0.2? Why?
The first step is to determine the probability that a customer will defualt. I tried drawing a tree diagram but I'm not sure what goes on the first level. Defaulting depends on missed payments, right? But wouldn't that mean that there's a 5% chance for anyone to default, reguardless of their missed payments?