📊 Bayes' Theorem Calculator
Calculate Bayesian posterior probabilities
Probability of A
Probability of B given A
Probability of B given not A
How Bayes' Theorem Works
- 1Enter the prior probability P(A), the likelihood P(B|A), and the false positive rate P(B|¬A).
- 2P(A|B) = P(B|A)·P(A) / [P(B|A)·P(A) + P(B|¬A)·P(¬A)] is computed.
- 3The posterior probability is displayed with a visual breakdown.
About Bayes' Theorem Calculator
Calculate posterior probabilities using Bayes' theorem. Enter prior probability, sensitivity, and false positive rate.
Frequently Asked Questions
What is a real-world example?
Medical testing: given a disease prevalence (prior), test sensitivity, and false positive rate, Bayes' theorem tells you the probability you actually have the disease after a positive test.
Why does the prior matter so much?
A low prior (rare event) means even a good test produces many false positives relative to true positives, yielding a surprisingly low posterior.