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026概率简单数值题short

Conflicting Two-Screen Update

题目

A loan is distressed with prior probability 0.3. Screen A flags a distressed loan with probability 0.8 and flags a healthy loan with probability 0.1. Any flagged loan then goes to screen B, which passes a distressed loan with probability 0.25 and passes a healthy loan with probability 0.70. Given that A flagged the loan and B did not pass it, what is the posterior probability the loan is distressed?

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