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 M, 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/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. 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 M, 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/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?
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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