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Statistics Calculators

Bayes' Theorem Calculator

Calculate the posterior probability P(A|B) from a prior probability and two conditional probabilities using Bayes' theorem.

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Posterior probability P(A|B)
Overall probability of evidence P(B)
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About the Bayes' Theorem Calculator

Bayes' theorem describes how to update the probability of a hypothesis (A) after observing new evidence (B). It combines your prior belief with how likely the evidence is under each scenario to produce an updated, "posterior" probability.

Formula: P(A|B) = [P(B|A) × P(A)] ÷ [P(B|A) × P(A) + P(B|not A) × P(not A)]

This is the foundation of medical test interpretation (why a positive result on a rare disease test can still be more likely a false positive than a true one), spam filtering, and countless other diagnostic and machine-learning applications.

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