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References for Conditional Probability and Independence

Curated resources to deepen your understanding of conditional probability, tree diagrams, independence, and Bayes' theorem.

Wikipedia Articles

  1. Conditional probability - Wikipedia - Thorough explanation of how knowing one event has occurred changes the probability of another event, with the formal definition and numerous worked examples.

  2. Bayes' theorem - Wikipedia - Covers the theorem that allows us to reverse conditional probabilities, including medical testing examples and the importance of base rates in interpreting results.

  3. Independence (probability theory) - Wikipedia - Explains the mathematical definition of independent events and how to test for independence, clarifying the common confusion with mutually exclusive events.

Textbooks

  1. The Practice of Statistics by Daren S. Starnes, Josh Tabor, and Dan Yates - W.H. Freeman (2018) - Chapter coverage of conditional probability includes excellent two-way table examples and step-by-step guidance on constructing and interpreting tree diagrams.

  2. Introduction to Probability by Joseph K. Blitzstein and Jessica Hwang - CRC Press (2019) - Rigorous yet accessible treatment of conditional probability and Bayes' theorem with intuitive explanations that build deep understanding.

Online Resources

  1. Khan Academy: Conditional Probability - Khan Academy - Video lessons walking through conditional probability calculations from two-way tables and Venn diagrams, with practice problems that provide instant feedback.

  2. Brilliant.org: Bayes' Theorem - Brilliant - Interactive lessons that build intuition for Bayesian reasoning through puzzles and real-world scenarios like medical testing and spam detection.

  3. 3Blue1Brown: Bayes theorem, the geometry of changing beliefs - YouTube - Visually stunning explanation of Bayes' theorem using geometric representations that make the mathematics feel intuitive rather than formulaic.

  4. Better Explained: An Intuitive Explanation of Bayes' Theorem - Better Explained - Uses everyday language and multiple analogies to explain why base rates matter so much when interpreting conditional probabilities.

  5. Arbital: Bayes' Rule Guide - Arbital - Comprehensive, interactive guide to Bayesian reasoning with worked examples showing common reasoning errors and how to avoid them.