taxicab problem

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The following problem of probability judgement, introduced in a book chapter in 1977 by the Israeli psychologists Amos Tversky (1937–96) and Daniel Kahneman (born 1934) to demonstrate the base-rate fallacy. A taxicab was involved in a hit-and-run accident at night. Only the Green and Blue cab companies operate in the city, where 85 per cent of the cabs are Green and 15 per cent are Blue. A witness identified the cab as Blue, and when tested under similar conditions was able to identify 80 per cent of both Blue and Green cabs correctly. What is the probability that the cab involved in the accident was Blue? The modal and median judgement was 80 per cent, which coincides with the reliability of the witness but ignores the relative frequency of Blue and Green cabs (the base rate). The correct answer, worked out from Bayes' theorem, is .41 or 41 per cent, which is much closer to the base rate.

Subjects: Psychology.

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