How can you tell if a question is Bayes Thereom?

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APersonYo
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A bank classifies borrowers as high risk or low risk. 15% of its loans are made to those classified as high risk. Of all loans, 5% are in default and 40% of those in default were made to high-risk borrowers. What is the probability that a high-risk borrower will default?

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old_engineer
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Bayes’ theorem usually raises its head when we know P(A given B) and need to find the value of P(B given A). This question is a case in point. Let P(H) be the probability that a borrower is in the high risk group and P(D) be the overall probability of default. The question gives us P(H given D) and asks us for P(D given H).
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