12. A local bank is reviewing its credit card policy. In the past, 5% of the ban

Question

12. A local bank is reviewing its credit card policy. In the past, 5% of the bank’s credit card holders have defaulted (i.e., a credit card holder fails to make a payment on the credit card debt for 180 days). The bank further found that for customers who do not default, the probability of missing one monthly payments is 0.20. Of course, for customers who do default, the probability of missing one monthly payments is 1. Given this information, calculate

(1) (4 points) What is the probability that a randomly selected customer misses one monthly payment? [Hint: consider using the law of total probability]

(2) (4 points) Given that a customer missed one monthly payment, what is the probability that he/ she will default? [Hint: consider using Bayes Rule]

Explanation / Answer

P(default) = 0.05

P(not default) = 1 - 0.05 = 0.95

P(missing one monthly payments | default) = 1

P(missing one monthly payments | not default) = 0.2

1) P(missing one monthly payments) = P(missing one monthly payments | default) * P(default) + P(missing one monthly payments | not default) * P(not default)

                                                 = 0.05 * 1 + 0.2 * 0.95

                                                 = 0.24

2) P(default | missing one month payments) = P(missing one monthly payments | default) * P(default) / P(missing one monthly payments)

                                                             = 0.05 * 1 / 0.24

                                                             = 0.2083

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