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During an audit, a finance company found that 1% of their loans are defaulted (not completely...

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 nondefaulted 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)

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Answer #1

P(loan made to poor credit risk)=P(defaulted and made to poor credit risk)+P(not defaulted and made to poor credit risk)

=0.01*0.3+0.99*0.1=0.102

P(hence defaulted given loan made to poor credit risk )=P(defaulted and made to poor credit risk)/P(loan made to poor credit risk)

=0.01*0.3/0.102 =0.0294

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