Validate and calculate three-event probabilities from mutual independence or a full set of pairwise and triple intersections.
How to use this tool
- Choose the event or model and review the assumptions below.
- Enter the labeled inputs. Probability inputs are percentages from 0 to 100, not decimal fractions.
- Select Calculate and read the labeled outputs.
- Change an input and calculate again; Reset restores the example inputs.
Calculation method
Union=a+b+c−ab−ac−bc+abc. The eight disjoint atoms determine none, exactly one, exactly two and all three.
Assumptions and limits
Pairwise independence alone does not imply mutual independence. In known-intersection mode all eight atoms must be nonnegative and sum to one; individual pair checks are insufficient.
Worked example
Three mutually independent 50% events have union 87.5%, exactly one 37.5%, exactly two 37.5%, all three 12.5% and none 12.5%.
Worked reading and practical questions
- Three-Event Inclusion–Exclusion Through Eight Disjoint Cases
- Pairwise Independent Does Not Mean Mutually Independent
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Frequently asked questions
What does this calculator assume?
Pairwise independence alone does not imply mutual independence. In known-intersection mode all eight atoms must be nonnegative and sum to one; individual pair checks are insufficient.
How do I enter and update the inputs?
Use the labeled fields, then select Calculate. Percent fields use 0 to 100. After editing, calculate again; Reset restores the example inputs.