Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-13
How statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Conditional probability for
Definition
Let and be events in a finite probability space with . The conditional probability of given is No value is assigned to when .
Depends on
Used by
- A loaded die as a nonuniform finite probability space Example
- Bayes' theorem for choosing one of two urns and observing a colour Example
- The conditional-probability induction underlying the Lovász Local Lemma Lemma
- The multiplication rule and finite chain rule for conditional probability Theorem
- Two positive-probability events are independent exactly when conditioning on either leaves the other's probability unchanged Theorem
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 31 results over 10 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.
Sources
- C. M. Grinstead and J. L. Snell, Introduction to Probability, 2nd ed., Section 4.1 (standard reference, not scraped)
- H. Pishro-Nik, Introduction to Probability, Statistics, and Random Processes, Section 1.4 (standard reference, not scraped)