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P(D₂) = P(M/D₁)= a. Given that a customer missed one or more monthly payments, compute the posterior probability that the customer will default, P(D1/M). b. 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?

P(D₂) = P(M/D₁)= a. Given that a customer missed one or more monthly payments, compute the posterior probability that the customer will default, P(D1/M). b. 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?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 42E
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3. Dagupan Bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past, approximately 5% of cardholders defaulted, leaving the bank unable to collect 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 did not default. Of course, the probability of missing a monthly payment for those who default is 1. Letting My be the event that a customer missed payment, D, be the event that a customer holder defaults, and D₂ be the event that a customer does not default. P(D₁) = P(M/L /D₂) = P(D₂) = P(M/D₁) = a. Given that a customer missed one or more monthly payments, compute the posterior probability that the customer will default, P(D₁/M). b. 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? 3
Transcribed Image Text:3. Dagupan Bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past, approximately 5% of cardholders defaulted, leaving the bank unable to collect 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 did not default. Of course, the probability of missing a monthly payment for those who default is 1. Letting My be the event that a customer missed payment, D, be the event that a customer holder defaults, and D₂ be the event that a customer does not default. P(D₁) = P(M/L /D₂) = P(D₂) = P(M/D₁) = a. Given that a customer missed one or more monthly payments, compute the posterior probability that the customer will default, P(D₁/M). b. 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? 3
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