Day 51 of 150 Logic Difficulty 6/10

Base-rate neglect: Bayes says 41%, intuition says 80%

Quick answer

Base-rate neglect: Bayes says 41%, intuition says 80%. Today's question (Base-rate neglect) asks about a finding from Bar-Hillel, M. in 1980. The correct option is ~41% — full explanation, primary source, and glossary cross-links below.

Today's question

In the classic "cab problem," a witness identifies a cab as Blue with 80% reliability, in a town where 85% of cabs are Green. Most participants estimate the probability the cab really was Blue at far above the Bayesian answer of:

  1. A ~12%
  2. B ~41%
  3. C ~59%
  4. D ~80%
Reveal the answer and explanation

Correct: B — ~41%

Tversky & Kahneman's cab problem and Bar-Hillel's analyses of base-rate neglect are classic demonstrations that people anchor on the witness's 80% reliability and largely ignore the prior — the 85:15 base rate of Green-to-Blue cabs. Bayes's rule weights the witness's evidence by the prior, yielding a posterior probability of about 41% that the cab was Blue. Most untrained participants give answers near 80%. The error is robust across statisticians, doctors, and judges, and underlies miscalibration of forensic and medical evidence.

About the source

Bar-Hillel, M. (1980). The base-rate fallacy in probability judgments. Acta Psychologica, 44(3), 211–233.

Every Cognition Bible question cites a primary source — a paper, book chapter, or monograph that exists, that we can point to on Google Scholar, and whose finding the question accurately summarizes. No fabricated authority strings, no name-drops without paper-level grounding.

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