Problem 2: Your company is preparing to roll out a fancy new facial recognition tool for detecting criminals from photographs, marketed as EyeOfSauron or E.O.S. Assume that one in a hundred residents of Oceania is a criminal. Each input photograph contains on Oceania resident. If the resident is a criminal, E.O.S. predicts correctly (CRIMINAL) with 80% probability and incorrectly (INNOCENT) with 20% probability. If the resident is not a criminal, E.O.S. predicts correctly (INNOCENT) with 95% probability and incorrectly (CRIMINAL) with 5% probability. Given that E.O.S. predicts a resident is CRIMINAL, what is the probability that they are actually a criminal? There is no need to simplify fractions. (Many people guess far too high; this bias is known as base rate neglect).

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