Bayes' Theorem Calculator
Apply Bayes' theorem to compute a posterior probability.
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Introduction
Bayes' Theorem Calculator — Apply Bayes' theorem to compute a posterior probability. Enter P(B|A), P(A), P(B) to get an instant, accurate result.
Formula
Bayes' theorem: P(A|B) = P(B|A) × P(A) / P(B), updating the prior probability P(A) using new evidence B.
Step-by-step
- Enter the P(B|A).
- Enter the P(A).
- Enter the P(B).
- Click Calculate to see your result instantly.
Real-world example
Example: With P(B|A) = 0.9, P(A) = 0.01, P(B) = 0.1, the Bayes' Theorem Calculator gives P A Given B: 0.09.
Frequently Asked Questions
What do the terms in the formula represent?
P(A) is the prior probability of A, P(B|A) is the likelihood of the evidence given A, P(B) is the overall probability of the evidence, and P(A|B) is the resulting posterior probability.
What is Bayes' theorem used for?
Common applications include medical test accuracy, spam filtering, and any situation where you need to revise a probability estimate in light of new evidence.
What inputs does the Bayes' Theorem Calculator need?
You'll need to provide: P(B|A), P(A), P(B). All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Bayes' Theorem Calculator?
The Bayes' Theorem Calculator applies the formula exactly as calculated — Bayes' theorem: P(A|B) = P(B|A) × P(A) / P(B), updating the prior probability P(A) using new evidence B. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Bayes' Theorem Calculator free to use?
Yes, the Bayes' Theorem Calculator is completely free, requires no signup, and runs instantly in your browser.
About the Bayes' Theorem Calculator
The Bayes' Theorem Calculator uses a real, verifiable formula — Bayes' theorem: P(A|B) = P(B|A) × P(A) / P(B), updating the prior probability P(A) using new evidence B. — so results are accurate every time, not an approximation.