Question

# his is a problem that can be solved using Bayes' theorem. Narrative: A local bank reviewed...

his is a problem that can be solved using Bayes' theorem.

Narrative:

A local bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past, 5% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence management established a prior probability of 0.05 that any card holder will default. the bank also found that the probability of missing a monthly payment for those who default is 1.0. For customers who do not default, the probability of missing a monthly payment is 0.02.

Given that the customer missed one or more monthly payments, compute the following:

a) posterior probability that a customer will default.

b) posterior probability that a customer will miss a payment.

c) How would the bank management use this information?

I recommend that you start by drawing a decision tree and assigning probabilities to each of its branches, then apply the Bayesian theorem. See the part supplier example in Section 4.5 for guidance. Carefully label each event and assign prior, conditional, joint and posterior probabilities to each event (you may use a tabular approach in Excel to make sure you don't make any arithmetical mistake). Show all your work

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