Bayes' Theorem Calculator

Calculate conditional probability P(A|B) using priors and likelihoods.

Unconditional Probabilities (Priors)

Probability that the hypothesis A is true before evidence
P(not A) = 0%

Conditional Probabilities (Likelihoods)

Probability of evidence B, GIVEN A is true (Sensitivity)
Probability of evidence B, GIVEN A is false
Posterior Probability P(A|B)

0%

Chance that A is true given B occurred

Probability Tree

A (0%)
B: 0%
P(A∩B)=0.00%
~A (0%)
B: 0%
P(~A∩B)=0.00%
P(A|B) = P(A∩B) / [P(A∩B) + P(~A∩B)]

Contextual Interpretation

If 0% of the population has a condition, and a test is 0% accurate (sensitivity), with a 0% false positive rate...

A person testing positive only has a 0% chance of actually having the condition.

Documentation

Bayes' Theorem

Bayes' theorem describes probability of an event, based on prior knowledge of conditions that might be related to the event.

Bayes' Theorem

Total Probability

Posterior

Frequently Asked Questions
How to Use

About the Bayes Theorem Calculator

What it calculates

This bayes theorem calculator solves mathematical and statistical problems using standard formulas. Calculate conditional probability P(A|B) using priors.

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Bayes Theorem Calculator.

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