The Taxi Cab Problem
In a city, 85% of cabs are Green and 15% are Blue. A witness to a hit-and-run identifies the cab as Blue, and testing shows the witness correctly identifies cab colors 80% of the time under similar conditions. What is the probability the cab was actually Blue? Express as a fraction.
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Source: The taxicab problem, from Daniel Kahneman and Amos Tversky's work on base-rate neglect (1972 onward). Statement written for AxiomIQ.