Feynman teaching note

Bayes' Theorem

SubjectMath

Area tags

Math

Bayes' theorem is a rule for updating a belief when new evidence arrives. Start with a prior (how likely something is before evidence), see some evidence, end with a posterior (how likely it is now). The famous trap is the rare-disease test. Suppose a disease affects 1 in 1,000 people, and a test is 99% accurate. You test positive. Are you 99% likely to be sick? No. Out of 1,000 people, 1 is truly sick (and tests positive), but about 10 healthy people also test positive by error. So among the ~11 positives, only 1 is actually sick: roughly 9%, not 99%. The lesson: a test result must be weighed against how rare the thing was to begin with. Rare priors can drown a good test in false positives.

Same topic, fresh practice—does not count as an adaptation.

Practice building on this note. If you publish, it can show “Based on” and add an adaptation.

Feedback & gaps

Clarity score: 84/100How well you know it: Can use it anywhere

Re-explain the rare-disease result to a friend who insists a 99% accurate positive means 99% chance of being sick.

Doesn't show the actual formula linking prior, likelihood, and posterior.
Could name base-rate neglect as the cognitive bias involved.

How I worked through the gaps

Why isn't a positive test 99% conclusive?

Base-rate neglect.

Q1In a group of 1,000, how many healthy people test positive by mistake vs how many truly sick test positive?

YouAbout 10 healthy false positives vs 1 true positive.

CoachRight, so most positives come from the huge healthy group. The rare prior dominates.

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