Enter prior P(A), likelihood P(B|A), and evidence P(B).

Bayes' theorem is a fundamental principle in probability theory that describes how to update the probability of a hypothesis based on new evidence. The theorem is expressed as: P(A|B) = P(B|A) · P(A) / P(B), where P(A) is the prior probability (initial belief before evidence), P(B|A) is the likelihood (probability of evidence given the hypothesis), P(B) is the marginal probability of evidence (total probability), and P(A|B) is the posterior probability (updated belief after evidence). This theorem is widely used in statistics, machine learning, medical diagnostics, spam filtering, and decision-making. It provides a mathematical framework for reasoning under uncertainty. The calculator also computes Bayes Factor (likelihood ratio), which quantifies the strength of evidence, and prior/posterior odds, which help interpret the results in terms of betting odds or risk assessment.

1. Enter the Prior P(A) – initial probability of hypothesis A (0–100%).
2. Enter the Likelihood P(B|A) – probability of evidence B given A (0–100%).
3. Enter the Evidence P(B) – total probability of observing B (0–100%).
4. Click Calculate Posterior to update the probability.
5. The result shows posterior probability, Bayes Factor, and odds ratios.
6. Click Reset to restore default example values.