Bayes' Theorem Calculator
Update a probability with Bayes’ theorem from a prior, a true-positive rate and a false-positive rate, with the full working.
Update a probability with Bayes’ theorem from a prior, a true-positive rate and a false-positive rate, with the full working.
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Bayes’ theorem updates the probability of a hypothesis after seeing evidence. The classic use is a diagnostic test: given how common a condition is and how reliable the test is, how likely is it that a positive result is a true positive?
The answer is often surprising — when a condition is rare, even an accurate test produces mostly false positives.
Example
P(A) = 0.01, P(B|A) = 0.9, P(B|not A) = 0.05
→ P(A|B) ≈ 0.1538
Bayes’ theorem with the denominator expanded by the law of total probability.