Question: Question 4 (12 points) Listen (12 points) A local bank is reviewing its credit-card policy with a view toward recalling some of its credit cards.

Question 4 (12 points) Listen (12 points) A local bank is reviewing its credit-card policy with a view toward recalling some of its credit cards. In the past, approximately 2.85% of cardholders have defaulted and the bank has been unable to collect the outstanding balance. Hence, management has established a prior probability of 2.85% that any particular cardholder will default. The bank has further found that the probability of missing one or more monthly payments is 15.25% for customers who do not default. Of course, the probability of missing one or more monthly payments for those who default is 1.00. Apply Bayes' theorem and compute the posterior probability a customer will default, given that he/she has missed one or more monthly payments. Clearly show your steps and manual (hand and a calculator) calculations in 4 decimal points. Question 3 (12 points) Listen (12 points) The Institute for Higher Education Policy studied the payback of college students loans due for payment six years after student-borrowers graduated from college. Suppose that an analysis of data compiled by the Institute indicates that the probability that a student with loan pays his/her loan satisfactorily is 62.35%; that a student with loan graduates from college is 65.38%; and that a student with loan graduates from college and satisfactorily pays his/her loan is 51.62%. If a student with loan did not graduate from college, what is the probability that he/she satisfactorily pays his/her loan? Clearly show your steps and calculations in 4 decimal points
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