Bayes' Theorem Calculator
Calculate P(A|B) using prior probability, likelihood, and marginal probability.
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Enter three values: the prior probability P(A), the likelihood P(B|A), and the marginal probability of evidence P(B). The calculator applies Bayes' theorem: P(A|B) = P(B|A) * P(A) / P(B). All inputs must be between 0 and 1. Results update instantly as you type.
About This Calculator
Bayes' theorem describes how to update the probability of a hypothesis given new evidence. It is foundational in medical testing, spam filtering, machine learning, and decision making. The theorem connects prior beliefs with observed data to produce a posterior probability.
Frequently Asked Questions
What is the prior probability?
The prior P(A) is your initial belief about the probability of A before observing evidence B. For example, the base rate of a disease in the population.
How do I find P(B), the marginal probability?
P(B) = P(B|A)*P(A) + P(B|not A)*P(not A). It is the total probability of observing the evidence across all hypotheses.
Why does Bayes' theorem matter in medical testing?
Because a positive test result does not mean you definitely have a condition. Bayes' theorem shows how the test accuracy and disease prevalence combine to determine the actual probability of having the condition.