# Bayes' Theorem Visualization

Explore How Evidence Updates Our Beliefs

> Canonical page: https://elysiatools.com/en/visualizations/bayes-theorem

- **Category:** Math

## Overview

Interactive exploration of Bayes' Theorem - the elegant formula for updating beliefs based on new evidence. Features classic disease detection case (false positive paradox) with adjustable prevalence, sensitivity, and false positive rate; population visualization (10,000 people grid); probability comparison charts; general Bayesian update with interactive prior, likelihood, and evidence sliders; animated belief update process; Venn diagram showing set relationships; and key insights including prior importance, evidence updates beliefs, likelihood ratio power, and iterative updating. Understand how P(H|E) = P(E|H) × P(H) / P(E) transforms prior beliefs into posterior knowledge

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