---
id:"kb-2026-00194"
title:"Probability Theory"
schema_type:"TechArticle"
category:"computer-science"
language:"en"
confidence:"high"
last_verified:"2026-05-22"
generation_method: "human_only"
ai_models:["claude-opus"]
derived_from_human_seed:true


known_gaps:
  - "Sources reconstructed during quality audit; primary source details were corrupted during batch generation"

completeness: 0.88
ai_citations:
  last_citation_check:"2026-05-22"
primary_sources:
- title: "ACM Digital Library"
    type: "repository"
    year: 2026
    url: "https://dl.acm.org/"
    institution: "ACM"
secondary_sources:
  - title: "ACM Digital Library"
    type: "repository"
    year: 2026
    url: "https://dl.acm.org/"
    institution: "ACM"
---

## TL;DR

Probability theory quantifies uncertainty — fundamental to machine learning, statistics, cryptography, and randomized algorithms. Key concepts: random variables, probability distributions (Bernoulli, binomial, normal, Poisson), expectation, variance, Bayes' theorem, law of large numbers.

## Core Explanation

Bayes' Theorem: P(A|B) = P(B|A) * P(A) / P(B). Used in: Naive Bayes classifiers, Bayesian inference, spam filters. Probability mass function (PMF) for discrete variables; probability density function (PDF) for continuous. Central Limit Theorem: sum of independent random variables approaches normal distribution — reason why normal distribution appears everywhere.

## Further Reading

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