Math
Probability of either event
Calculate union probability for two events with a stated overlap.
Calculators / Math / Bayes theorem
Bayes theorem calculator
Update the probability of A after observing evidence by combining its prior probability with the evidence likelihood under A and under not-A.
On this page
Posterior probability30.77%
Evidence probability26%
Calculator controls
How to calculate
Update the probability of A after observing evidence by combining its prior probability with the evidence likelihood under A and under not-A.
Posterior probability = p*a/(p*a+(100-p)*b)*100 %; Evidence probability = (p*a+(100-p)*b)/100 %
Worked example
Prior probability (%): 10; Evidence probability given A (%): 80; Evidence probability without A (%): 20.
Posterior probability: 30.77 %; Evidence probability: 26 %.
Assumptions and limits
Update the probability of A after observing evidence by combining its prior probability with the evidence likelihood under A and under not-A. A and not-A must cover all possibilities. Enter probabilities, not counts; evidence probability must be nonzero.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Update the probability of A after observing evidence by combining its prior probability with the evidence likelihood under A and under not-A.
When this tool is useful
Posterior probability = p*a/(p*a+(100-p)*b)*100 %; Evidence probability = (p*a+(100-p)*b)/100 %
Understanding your inputs
| Input | What to enter |
|---|---|
| Prior probability (%) | Enter a number of at least 0 and no more than 100. |
| Evidence probability given A (%) | Enter a number of at least 0 and no more than 100. |
| Evidence probability without A (%) | Enter a number of at least 0 and no more than 100. |
Frequently asked questions
What assumptions does this calculation use?
Update the probability of A after observing evidence by combining its prior probability with the evidence likelihood under A and under not-A. A and not-A must cover all possibilities. Enter probabilities, not counts; evidence probability must be nonzero.
How is the result calculated?
Posterior probability = p*a/(p*a+(100-p)*b)*100 %; Evidence probability = (p*a+(100-p)*b)/100 %