The likelihood of getting a completely factual financial statement from credit c
ID: 3063061 • Letter: T
Question
The likelihood of getting a completely factual financial statement from credit card applicants in a
department store chain is 0.90. Eighty percent of the applicants filing factual applications prove to be
good credit risks. Only 30% of the applicants filing non-factual applications prove to be good credit
risks. A spot check of applications that you, as credit manager, have approved is begun.
(a) [10 points] If you are informed that a randomly selected applicant turned out to be a good
credit risk for the chain, how likely is it that the application was not completely factual?
(b) [10 points] If another applicant turned out to be a bad credit risk for the chain, how likely is it
that the application was factual?
Explanation / Answer
P(factual application) = 0.9
P(good credit risks | factual application) = 0.8
P(good credit risks | non factual application) = 0.3
a) P(good credit risks) = P(good credit risks | factual application) * P(factual application) + P(good credit risks | non factual application) * P(non factual application)
= 0.8 * 0.9 + 0.3 * (1 - 0.9)
= 0.75
P(non factual application | good credit ) = P(good credit risks | non factual application) * P(non factual application) / P(good credit risk)
= 0.3 * (1 - 0.9) / 0.75
= 0.04
b) P(bad credit risk) = 1 - P(good credit risk) = 1 - 0.75 = 0.25
P(bad credit risks | factual application) = 1 - P(good credit risks | factual application) = 1 - 0.8 = 0.2
P(factual application | bad credit risks) = P(bad credit risks | factual application) * P(factual application) / P(bad credit risk)
= 0.2 * 0.9 / 0.25
= 0.72
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