The likelihood of getting a completely factual nancial statement from credit car

Question

The likelihood of getting a completely factual nancial statement from credit card applicants in a department store chain is 0.90. Eighty percent of the applicants ling factual applications prove to be good credit risks. Only 30% of the applicants ling non-factual applications prove to be good credit risks. A spot check of applications that you, as credit manager, have approved is begun.
(a) 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) If another applicant turned out to be a bad credit risk for the chain, how likely is it that the application was factual?

F={ factual application}

Fc= { non-factual application}

G = {good credit}

Gc = {bad credit}

Pr[F] = 0.9 , Pr [Fc] = 0.1

Pr[GF] = 0.8

Pr [ G Fc] = 0.3

Explanation / Answer

a) P(Fc|G) =P(Fc)*P(G|Fc)/(P(Fc)*P(G|Fc)+P(F)*P(G|F)) =0.1*0.3/(0.1*0.3+0.9*0.8)=0.04

b)P(F|Gc) =P(F)*P(Gc|F)/(P(Fc)*P(Gc|F)+P(F)*P(Gc|F)) =0.9*0.2/(0.9*0.2+0.1*0.7)=0.72

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