Common Reasoning Errors

Base rate neglect occurs when people ignore the prior probability (base rate) of an event and focus only on the evidence. Kahneman and Tversky's taxi cab problem: 85% of cabs in a city are green, 15% are blue. A witness identifies a cab in an accident as blue. The witness correctly identifies colors 80% of the time. What is the probability the cab was blue? Most people say 80% (the witness accuracy). Bayes says: P(Blue|ID as Blue) = 0.80 × 0.15 / (0.80 × 0.15 + 0.20 × 0.85) = 0.12 / (0.12 + 0.17) = 41%. The base rate (only 15% of cabs are blue) dramatically reduces the probability despite the witness's 80% accuracy.