References: When one event tells you about another: conditional probability and independence

Source material

Source curriculum (structural mirror, cited as further study):
• Khan Academy, "Conditional probability and independence" (Statistics & Probability)
  Author: Sal Khan and the Khan Academy team
  Unit page: https://www.khanacademy.org/math/statistics-probability/probability-library/conditional-probability-independence
  License: CC BY-NC-SA 4.0
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Source-scope note: this lesson mirrors Khan's treatment of conditional
probability, the general multiplication rule, and independence, restated in
Clawdemy's voice with an original two-way diagnostic table and a card example.
The two-way table here deliberately sets up Bayes' theorem (the next lesson) by
showing P(positive | condition) and P(condition | positive) as different
numbers without yet writing the Bayes formula. The AI connections (classifiers
as P(label | inputs), language models as P(next word | previous words)) are
Clawdemy framing. Exact per-unit URLs are verified at promotion.

Read this next

• Khan Academy: Conditional probability and independence by Sal Khan and the Khan Academy team. The full unit this lesson mirrors, with videos and practice on conditional probability, dependence, and independence, free and CC-licensed. Drill the two-way-table computations here until restricting and dividing is automatic.

Going deeper

A short, durable list. Both are free.

• Khan Academy, “Probability” (within the course above). The previous lesson’s source. Revisit the multiplication rule to see how the general (conditional) form here extends the independent-only form there.
• Khan Academy, the Bayes’ theorem material (within the course above). The direct continuation: the machine for converting P(A given B) into P(B given A) correctly, which is the next Track 9 lesson and the formal version of lesson 1’s base-rate example.

Adjacent topics

Where this sits inside this track.

• Probability foundations. The previous lesson. Its independence caveat on the multiplication rule is exactly what this lesson lifts.
• Updating beliefs with evidence: Bayes’ theorem. The next lesson. The two-way table’s two different conditionals become Bayes’ theorem, which flips one into the other.
• Why AI runs on statistics. Lesson 1. The base-rate example there is the same structure as this lesson’s screening table; here you see precisely where the two conditionals diverge.