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Bayes Theorem Posterior Probability Calculator — result sheet
Calculate a posterior probability from prior probability, sensitivity, and specificity.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: P(condition|positive)=prior×sensitivity/[prior×sensitivity+(1−prior)×(1−specificity)].
The denominator includes true and false positive paths so the base rate remains visible.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Prior probability — minimum 0; maximum 1
- Sensitivity — minimum 0; maximum 1
- Specificity — minimum 0; maximum 1
Worked example
| Input | Value |
|---|---|
| Prior probability | 0.1 |
| Sensitivity | 0.9 |
| Specificity | 0.95 |
Posterior probability ≈66.67%.
Assumptions and limits
- Prior, sensitivity, and specificity are probabilities between zero and one.
- The test characteristics apply to the same population and event definition.
- Sampling bias, changing prevalence, dependence, and clinical or operational decisions are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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