Events occupy regions of one sample space. The shared region is the intersection; every covered region forms the union.
Aevent ABevent BA ∩ B shared
1EnterProvide the known values
2CalculateResults update automatically
3VerifyReview the details and units
Try an example
Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.
Statistics result
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What the independent events calculator is calculating
Mapping relationships between events. Unions, intersections, complements, exclusion, and independence describe different regions or relationships. Drawing the regions first prevents common addition-versus-multiplication mistakes.
1Define the sample space and events2Locate exclusive and shared regions3Apply the union, product, or bound rule
Probability rule
If independent, P(A∩B)=P(A)P(B).
Every probability must remain between 0 and 1, and overlapping regions must be jointly feasible. The calculator rejects combinations that violate the stated model.
How to interpret it
Independence means knowing one event occurred does not change the other event’s probability.
Model boundary: The calculator cannot establish independence from the two probabilities alone; the visitor must justify it from design or evidence.
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 independent events calculator works
If independent, P(A∩B)=P(A)P(B).
Independence means knowing one event occurred does not change the other event’s probability.
Worked example
Independent Events example
Independent probabilities 0.5 and 0.2 give intersection 0.1 and union 0.6.
If independent, P(A∩B)=P(A)P(B).
Supported inputs
Precision and limits
Model and design
The calculator cannot establish independence from the two probabilities alone; the visitor must justify it from design or evidence.
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
Independence means knowing one event occurred does not change the other event’s probability.
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.
