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031概率简单数值题short

Flagged but Then Cleared

题目

A borrower is high risk with prior probability 0.2. A fast model flags a high-risk borrower with probability 0.7 and flags a low-risk borrower with probability 0.1. Only flagged borrowers get a manual review. A high-risk flagged borrower passes manual review with probability 0.4, while a low-risk flagged borrower passes it with probability 0.7. Given that a borrower was flagged and then passed manual review, what is the posterior probability the borrower is high risk?

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