A local bank reviewed its credit card policy with the intention of recalling som

Question

A local bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past approximately 2% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a prior probability of.02 that any particular cardholder will default. The bank also found that the probability of missing a monthly payment is.10 for customers who do not default. of course, the probability of missing a monthly payment for those who default is 1. a. Given that a customer missed one or more monthly payments, compute the posterior probability that the customer will default (to 2 decimals). b. The bank would like to recall its card if the probability that a customer will default is greater than .10. Should the bank recall its card if the customer misses a monthly payment? Why or why not? Yes, the probability of default is greater than.10. Yes, the probability of default is less than.10. No, the probability of default is greater than.10. No, the probability of default is less than .10

Explanation / Answer

a) probability of missing monthly payment =P(customer will default and miss monthly payment +customer will not default and miss monthly payment )=0.02*1+(1-0.02)*0.1=0.118

hence probability of default given miss payment =0.02*1/0.118 =0.1695

b)Yes the probability of default is greater than 0.10

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