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 3% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a prior probability of .03 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.

Given that a customer missed one or more monthly payments, compute the posterior probability that the customer will default (to 2 decimals).

Explanation / Answer

P(default) = 0.03

P(not default) = 1 - 0.03 = 0.97

P(missing one month payment | not default) = 0.1

P(missing one month payment | default) = 1

P(missing one month payment) = P(missing one month payment | default) * P(default) + P(missing one month payment | not default) * P(not default)

                                                   = 1 * 0.03 + 0.1 * 0.97

                                                   = 0.127

P(default | missing one month payment) = P(missing one month payment | default) * P(default) / P(missing one month payment)

                                                                = 1 * 0.03 / 0.127

                                                                = 0.24

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