Bayes Theorem Calculator
Calculate posterior probability using Bayes’ theorem.
Bayes’ Theorem Formula
P(A|B) = P(B|A) × P(A) / P(B). Bayes’ theorem updates the probability of an event after considering related evidence.
How Bayes Theorem Updates Probability
Bayes theorem combines prior probability with new evidence to calculate an updated posterior probability.
Bayes Example
If a condition is rare but a test is highly accurate, the probability of truly having the condition after a positive result depends on both test performance and the original prevalence.
Why Base Rates Matter
Ignoring prior probability can lead to misleading conclusions. Bayes theorem makes the base rate explicit and shows how strongly new evidence changes the estimate.
Frequently Asked Questions
What is a prior probability?
It is the probability before new evidence is considered.
What is posterior probability?
It is the updated probability after considering evidence.
Is Bayes theorem only for medical tests?
No. It is used throughout statistics, machine learning and decision analysis.
Methodology and Practical Limits
Bayes’ theorem updates a prior probability using evidence: P(A|B)=P(B|A)P(A)/P(B). Results depend on the prior and likelihood assumptions, so changing either can materially change the posterior probability.