References: Updating beliefs with evidence: Bayes' theorem

Source material

Source curriculum (structural mirror, cited as further study):
• Khan Academy, "Probability" (Bayes' theorem material, Statistics & Probability)
  Author: Sal Khan and the Khan Academy team
  Unit page: https://www.khanacademy.org/math/statistics-probability/probability-library
  License: CC BY-NC-SA 4.0
Clawdemy's lessons are original prose that follows the pedagogical arc of this
material. We do not embed, reproduce, or transcribe Khan's text or videos; we
link out to the relevant unit as recommended further study. The non-commercial
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Source-scope note: this lesson mirrors Khan's Bayes' theorem material and
restates it in Clawdemy's voice. It deliberately re-derives lesson 1's
base-rate result (the 1-in-100 disease, 99% test, 50% posterior) so the
opener's preview, lesson 6's two-way table, and this formula form one arc. The
natural-frequencies-before-formula order, the two-positive-test update, and the
AI connections (naive Bayes, combining a detector with a base rate, Bayesian
updating) are Clawdemy framing. Exact per-unit URLs are verified at promotion.

Read this next

• Khan Academy: Probability (including Bayes’ theorem) by Sal Khan and the Khan Academy team. The unit this lesson draws on, with videos and practice on conditional probability and Bayes, free and CC-licensed. Work the tree-diagram and natural-frequency versions until the base-rate effect feels obvious.

Going deeper

A short, durable list. Both are free.

• Khan Academy, “Conditional probability and independence” (within the course above). The previous lesson’s source and the direct foundation for Bayes: the two-way table there is the same calculation, one step before the formula.
• Khan Academy, “Random variables” (within the course above). The bridge to the next phase: once you can reason about single events, random variables let you reason about whole distributions of outcomes, where Track 9 goes next.

Adjacent topics

Where this sits inside this track.

• When one event tells you about another: conditional probability and independence. The previous lesson. Its two different conditionals are exactly what Bayes converts between.
• Why AI runs on statistics. Lesson 1. The base-rate example previewed there is re-derived here with the full machinery; this lesson closes that arc.
• Random variables and expected value. The next lesson and the start of Phase 3 (Random variables and the distributions that matter). The track shifts from single events to whole distributions of outcomes.