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Statistics · Probability

Three-Event Probability Calculator

Analyze three overlapping events from individual, pairwise, and triple-intersection probabilities with full feasibility validation.

Statistics · Probability

Enter your statistical inputs

Private in-browser calculation · explicit assumptions
Events occupy regions of one sample space. The shared region is the intersection; every covered region forms the union.
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 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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Understand the probability

What the three-event probability 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.

Probability rule

P(A∪B∪C)=ΣP(single)−ΣP(pairwise intersections)+P(A∩B∩C).

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

Pairwise intersections include the triple intersection; converting them to disjoint regions prevents overlap from being counted twice.

Model boundary: All seven entered probabilities must define nonnegative disjoint regions whose complete union does not exceed one.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. 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.

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