A local bank is reviewing its credit-card policy with a view toward recalling so

Question

A local bank is reviewing its credit-card policy with a view toward recalling some of its credit cards. In the past, approximately 2.5% of cardholders have defaulted and the bank has been unable to collect the outstanding balance. Hence management has established a prior probability of 2.5% that any particular cardholder will default. The bank has farther found that the probability of missing one or more monthly payments is 10% 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 a monthly payment. Clearly show your steps and manual (hand and calculator) calculations in 4 decimal places, where possible.

Explanation / Answer

Ans:Bayes's theorm:

P(missing monthly payments/who do not default)=0.1

P(not missing monthly payments/who do not default)=1-0.1=0.9

P(missing monthly payments/who default)=1

P(not missing monthly payments/who default)=0

P(default)=0.025

P(not default)=1-0.025=0.975

P(default/missing monthly payment)=P(missing monthly payment/default)*P(default)/[P(missing monthly payment/default)*P(default)+P(missing monthly payment/not default)*P(not default)]

    P(default/missing monthly payment) =1*0.025/[1*0.025+0.1*0.975]=0.025/0.1225=0.2041

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.