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 three-event probability calculator works
P(A∪B∪C)=ΣP(single)−ΣP(pairwise intersections)+P(A∩B∩C).
Pairwise intersections include the triple intersection; converting them to disjoint regions prevents overlap from being counted twice.
Worked example
Three-Event Probability example
Individual probabilities 0.5, 0.4, 0.3 with pairwise intersections 0.2, 0.1, 0.1 and triple 0.05 give union 0.85.
P(A∪B∪C)=ΣP(single)−ΣP(pairwise intersections)+P(A∩B∩C).
Supported inputs
Precision and limits
Model and design
All seven entered probabilities must define nonnegative disjoint regions whose complete union does not exceed one.
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
Pairwise intersections include the triple intersection; converting them to disjoint regions prevents overlap from being counted twice.
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.
Continue calculating