When to use this calculator
Bayesian updating combines how common an event was before observing evidence with how likely that evidence is under each alternative.
Explore the probability & distributions calculators for other questions in this topic. For a related calculation, use the Binomial Mean Calculator: Find the expected number of successes across identical independent trials.
PUTTING IT INTO PRACTICE
Bayes Theorem: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Prior probability of A (%) | 10 |
| P(evidence given A) (%) | 80 |
| P(evidence given not A) (%) | 20 |
| Result | 30.769231 % |
- Check the input labels and enter the example values above.
- Apply the relationship: Posterior (%) = prior × likelihood A/(prior × likelihood A + (1−prior) × likelihood not A) × 100.
- The result is 30.769231 %, rounded for display.
How to interpret your result
The evidence must have nonzero total probability. Likelihood inputs are conditional probabilities.
A distribution model is an assumption about the process, not a guarantee about outcomes. Independence, constant probability and fixed interval definitions matter. Exactly-k probabilities differ from cumulative probabilities.
Frequently asked questions
Does exactly two successes mean two or more?
No. Exactly two counts only outcomes with two successes. Two or more is a cumulative probability covering several counts.
When is the bayes theorem calculator useful?
Bayesian updating combines how common an event was before observing evidence with how likely that evidence is under each alternative.
How do I use the bayes theorem calculator?
Enter prior probability of a (%), p(evidence given a) (%), p(evidence given not a) (%). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Posterior (%) = prior × likelihood A/(prior × likelihood A + (1−prior) × likelihood not A) × 100.
What should I check before using the result?
The evidence must have nonzero total probability. Likelihood inputs are conditional probabilities.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see NIST: probability distributions ↗. This is a topic reference, not an external review or endorsement of this tool.
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