Answer to Question #235863 in Statistics and Probability for Excoba

Question

4. a. Distinguish between a null hypothesis and an alternative hypothesis. (6rnarks)

A local bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past approximately 50/0 of cardholders defaulted, leaving the bank unable to collect the outstanding balance.

Hence, management established a prior probability of 0.05 that any particular cardholder will default. The bank also found that the probability of missing a monthly payment is 0.20 for customers who do not default. Of course, the probability of missing a monthly payment for those who default is 1.

i. Given that a customer missed one or more monthly payments, compute the posterior probability that the customer will default. (10 marks) ii. The bank would like to recall its card if the probability that a customer will default is greater than 0.20. Should the bank recall its card if the customer misses a monthly payment? Why or why not? (4 marks)

Answer 1

1) Given P(default) = .07, thus, P(no default) = 0.93

P(missing a monthly payment / no default) = 0.20

P(missing a monthly payment / default) = 1.0

P(default/ missing a monthly payment $= \frac{(1*0.07) }{(1*0.07) + (0.20*0.93)} = 0.27344 =27.34$

2) Yes, because from the computations above in Part-1, the probability of a customer may default is 27.34% if a customer misses a monthly payment for one month, however, the bank can only afford to have 20% of its customers default, then the bank would immediately stop providing the service to these customers in such a scenario.