P(A|B)Bayes Theorem Calculator
Classic medical screening example: what is the probability of disease given a positive test?
Population prevalence
P(+|Disease)
P(−|No disease)
Bayes' Theorem describes how to update the probability of a hypothesis given new evidence. Named after Rev. Thomas Bayes (1702–1761), it is the mathematical foundation of Bayesian statistics and is central to medical diagnosis, spam filtering, machine learning, and forensic science. The theorem shows why even a highly accurate test can produce mostly false positives when the disease is rare — this is the base rate fallacy.
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