A physical exam is administered to all new inmates at a prison. Suppose that 80%

Question

A physical exam is administered to all new inmates at a prison. Suppose that 80% of all healthy individuals pass this exam, 60% of all individuals with minor ailments pass, and 30% of all prisoners with serious ailments also pass. Suppose that 25% of these new prisoners are actually in good health (event E1), 50% have minor ailments (E2), and 25% have major health issues (E3). Given that an inmate passes this physical (event B), what is the posterior probability that the inmate is in good health? Compute it using Bayes’ Theorem, not by the enumeration of Full Joint Probability Distribution.

Explanation / Answer

what is the posterior probability that the inmate is in good health?

P( good health ) = 0.80 * 0.25 + 0.60 * 0.50 + 0.25 * 0.30 = 0.575

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