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The medical test paradox, and redesigning Bayes' rule

3Blue1Brown · explainer · Watch on YouTube

Probability & game theoryRecreational & visual math

What it is

3Blue1Brown explains why positive results on accurate medical tests are often false positives, and reframes Bayes' rule using likelihood ratios (Bayes factors) to update odds. It uses visual examples to make the reasoning intuitive.

Why Hacker News recommends it

HN's go-to link whenever Bayesian reasoning, base rates or imperfect tests come up.

  • 4 people recommended it
  • 4 different months
  • 1 strong recommendations
  • first 2020, last 2025

What HN commenters said

  1. “All his videos are absolutely phenomenal - the best educational content I've seen on YouTube.”

    Engaging explanation of the medical test paradox and Bayes' rule.

    drewmate, 2020-12 · Strong recommendation · in “1937 film explains how a car differential works”

  2. “is a brilliant introduction to the concept”

    Introduction to updating odds from imperfect tests.

    kilotaras, 2021-01 · Recommendation · in “U.S. to require negative Covid-19 tests for international air passengers”

  3. “3Blue1Brown explains it well.”

    Explains why rare conditions make positives mostly false.

    andersrs, 2024-01 · Recommendation · in “The cancer that some doctors don't want to call cancer”

  4. “I really like this video [1] from 3blue1brown”

    Thinking of significance as a probability update.

    V__, 2025-08 · Recommendation · in “Everything is correlated (2014–23)”

Excerpts from Hacker News comments, linked to the originals. Summaries and labels were written by a language model from those comments.

Topics: bayes factor, likelihood ratio, base rate, medical tests, probability

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