Bayes’ Theorem
Update a prior probability from true-signal and false-signal rates.
Your numbers
Posterior probability
Inputs are probabilities you supply; this tool does not infer them from a diagnosis or a real-world population.
Scenario comparison
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Formula
P(A|B)=P(B|A)P(A)/(P(B|A)P(A)+P(B|¬A)P(¬A))
Update a prior probability from true-signal and false-signal rates.
Worked example
- Prior probability (%)
- 1
- Signal rate when true (%)
- 99
- Signal rate when false (%)
- 5
- Posterior probability
- 16.6666666667 %
- Overall signal probability
- 5.94 %
Scope and limitations
Inputs are probabilities you supply; this tool does not infer them from a diagnosis or a real-world population.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: 732fc1675057 · Example checked: