You must solve it on Baye’s Theorem. John goes to Schools First Credit Union for

Question

You must solve it on Baye’s Theorem.

John goes to Schools First Credit Union for a loan. The bank knows that there is a 4% chance that a customer will default on (not pay back) the loan. The bank runs John’s credit check to find if it will be favorable or unfavorable to give him loan. From historical records, the bank also know that

P(favorable report being received | customer will default) = 2.5% and P(favorable report | customer will not default) = 99%. If a favorable report is received, what is the probability that John will default on the loan?

Explanation / Answer

P(default)=.04

P(not default)=1-.04=.96

P(favourable/default)=.025

P(favourable/not default)=.99

Using Bayes theorem

P(default/favourable)=[P(default)*P(favourable/default)]/[P(default)*P(favourable/default)+P(not default)*P(favourable/not default)]

=(.04*.025)/(.04*.025+.96*.99)

=.001051083

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