Tuesday, November 23, 2010

Back to Base-ics

Another base rate problem (from Chapter 10 of Judgment under Uncertainty: Heuristics and Biases - "Evidential impact of base rates" by Tversky and Kahneman):

A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. You are given the following data:

(a) 85% of the cabs in the city are Green and 15% are Blue.

(b) A witness identified the cab as Blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colours 80% of the time and failed 20% of the time.

What is the probability that the cab involved in the accident was Blue rather than Green?

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