Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the law of total probability calculator works
For exhaustive disjoint cases Aᵢ, P(B)=ΣP(Aᵢ)P(B|Aᵢ).
Each path contribution shows how prevalence and conditional likelihood jointly determine the overall event rate.
Worked example
Law of Total Probability example
Cases with priors 0.4 and 0.6 and conditional probabilities 0.2 and 0.5 give P(B)=0.38.
For exhaustive disjoint cases Aᵢ, P(B)=ΣP(Aᵢ)P(B|Aᵢ).
Supported inputs
Precision and limits
Model and design
Case probabilities must be nonnegative, align with conditionals, total one, and form mutually exclusive exhaustive cases.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Each path contribution shows how prevalence and conditional likelihood jointly determine the overall event rate.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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