Question: A major 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 established a prior probability of 0.05 that any particular cardholder will default. The bank has further found that the probability of missing one or more monthly payments is 0.2 for customers who do not default. Of course, the probability of missing one or more payment by those who do not default is 1.

1. Given that a customer has missed a monthly payment, calculate the probability that the customer will default.
2. The bank would like to recall its card if the probability that a customer will default is 0.2. Should the bank recall its card if a customer misses a monthly payment? Justify your answer.

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