In This Article The Question The Intuition Trap: The Base Rate Fallacy The Mathematical Proof Python Simulation: 1,000,000 Trials Litigation Application: When Juries Get the Math Wrong The Question A cab was involved in a hit-and-run accident at night. Two cab companies operate in the city: the Green company and the Blue company. You are given the following facts: 85% of the cabs in the city are Green, and 15% are Blue. A witness identified the hit-and-run cab as Blue. The court tested the witness under the same conditions that existed on the night of the accident and found that the witness correctly identifies each color 80% of the time and fails 20% of the time. Given this information, what is the exact probability that the cab involved in the accident was actually Blue? This problem was formulated by Amos Tversky and Daniel Kahneman — the architects of behavioral economics — as a demonstration of one of the most durable cognitive failures in human reasoning: the Base Rate Fallacy.…