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 6% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a prior probability of .06 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?

Explanation / Answer

Ans:

P(default)=0.06

P(don't default)=1-0.06=0.94

P(missing a monthly payment/who don't default)=0.1

P(missing a monthly payment/who default)=1

Now calculate:

P(missing a monthly payment)=1*0.06+0.1*0.94=0.06+0.094=0.154

a)

P(default/missing a monthly payment)

=P(missing a monthly payment/default)*P(default)/P(mssing a monthly payment)

=1*0.06/0.154

=0.3896

b)As the probability of default given that customer missed monthly payment is 0.3896>0.1,So,bank should recall its card.

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