A local bank reviewed its credit-card policy with the intention of recalling some of its credit cards. In the past, approximately 8% of cardholders defaulted, leaving the bank unable to collect the outstandiing balance. Hence, management established a prior probability of 0.08 that any particular cardholder will default. The bank also found that the probability of missing a monthly payment is 0.15 for customers who do not default. Of course, the probability of missing a monthly payment for those who default is 1.

let D1 represent the event that a customer defaults

D2 respresent the event that a customer does not default

M represent the event that a customer misses a payment

1. the joint probability of D1 and M =

2. the joint probabikity of D2 and M =

3. the probability of a random customer would miss a payment, that is P(M) =

4. given thag a customer missed a monthly payment, compute the posterior probability that the customer will default thag is P(D1 | M) =

5. the bank would like to recall its credit card if the probability that a customer will default is greater than 0.25. should the bank recall its credit card if the customer missing a monthly payment ( Yes or No)