Statistics & Probability Calculators
Bayes' Theorem Calculator
Update a prior probability after observing evidence, with the derivation shown.
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What is Bayes' Theorem?
Bayes' theorem revises a belief in light of evidence: P(A | B) = P(B | A)P(A) ÷ [P(B | A)P(A) + P(B | ¬A)P(¬A)]. It explains why a very accurate test on a rare condition still mostly reports false positives — the base rate dominates.
How it works
The numerator is the probability of the evidence via the true hypothesis, the denominator totals it over both hypotheses, and the ratio is the posterior. All three substitutions are printed because the base-rate step is where hand calculations usually go wrong.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
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