Question

During an audit, a finance company found that 1% of their loans are defaulted (not completely repaid). When an individual applies for a loan, the finance company runs a credit check on the individual. The company finds that 30% of defaulted loans went to poor credit risks, 40% went to fair credit risks, and 30% went to good credit risks. Of the non-defaulted loans, 10% went to poor risks, 40% went to fair risks, and 50% went to good risks. Find the probability that a loan made to a poor credit risk will be defaulted. (answer: 0.0294)

Answer 1

Solution:-

Given

P(Defaulted) = 0.01,

so, P(not Defaulted) =(1-0.01)= 0.99

P(Poor|Defaulted) = 0.30

P(Fair|Defaulted) = 0.40

P(Good|Defaulted) = 0.30

P(Poor|not Defaulted) = 0.10

P(Fair|not Defaulted) = 0.40,

P(Good|not Defaulted) = 0.50

P(Poor) = P(Poor|Defaulted)*P(Defaulted) + P(Poor|not Defaulted)*P(not Defaulted)

=( 0.30*0.01 + 0.10*0.99)

= 0.003+0.099

= 0.102
Now,

P(Defaulted|Poor) = P(Poor|Defaulted)*P(Defaulted)/P(Poor)

= (0.30*0.01)/0.102

= 0.029412

=0.0294 ..............ans