Calculator inputs
Use decimal probabilities between 0 and 1. Example: 0.35 means 35%.
Example data table
These sample values show how inclusive, exclusive, and complement probabilities can be organized before submission.
| Scenario | P(A) | P(B) | P(C) | P(A∩B) | P(A∩C) | P(B∩C) | P(A∩B∩C) | P(A∪B∪C) |
|---|---|---|---|---|---|---|---|---|
| Sample 1 | 0.60 | 0.50 | 0.40 | 0.30 | 0.22 | 0.18 | 0.10 | 0.90 |
| Sample 2 | 0.35 | 0.45 | 0.25 | 0.14 | 0.09 | 0.10 | 0.05 | 0.77 |
Formula used
The calculator applies inclusion-exclusion logic for three events, then breaks the overlap structure into exclusive regions and conditional ratios.
- Union: P(A∪B∪C) = P(A) + P(B) + P(C) − P(A∩B) − P(A∩C) − P(B∩C) + P(A∩B∩C)
- None: P(None) = 1 − P(A∪B∪C)
- Only A: P(A) − P(A∩B) − P(A∩C) + P(A∩B∩C)
- Exactly one: Only A + Only B + Only C
- Exactly two: [P(A∩B) − P(A∩B∩C)] + [P(A∩C) − P(A∩B∩C)] + [P(B∩C) − P(A∩B∩C)]
- Conditional example: P(A|B) = P(A∩B) ÷ P(B), provided P(B) > 0
- Independence mode: P(A∩B) = P(A)×P(B), P(A∩C) = P(A)×P(C), P(B∩C) = P(B)×P(C), P(A∩B∩C) = P(A)×P(B)×P(C)
How to use this calculator
- Enter P(A), P(B), and P(C) as decimals between 0 and 1.
- Leave independence mode off if you already know the pairwise and triple overlaps.
- Turn independence mode on when events are assumed independent and overlaps should be generated automatically.
- Press Calculate Probability Set to display results above the form.
- Review the union, none, exact-one, exact-two, conditional values, and independence diagnostics.
- Use the CSV or PDF buttons to export the currently displayed result set.
Frequently asked questions
1. What does the calculator solve?
It evaluates three-event probability structures, including union, none, only-one, exactly-two, all-three, and several conditional probabilities from your entered overlaps.
2. When should I enable independence mode?
Enable it when A, B, and C are modeled as independent events. The calculator then computes pairwise and triple intersections from the marginal probabilities.
3. Why can my inputs be rejected?
Some combinations are impossible. For example, an intersection cannot exceed either single-event probability, and the final union cannot be greater than 1.
4. What is the difference between exactly two and at least two?
Exactly two counts outcomes that belong to two events but excludes the triple overlap. At least two includes both the exactly-two region and all three together.
5. Can I use percentages instead of decimals?
Enter decimals only. Convert percentages first, so 35% becomes 0.35. This keeps formulas consistent and avoids scaling errors.
6. What does P(None) mean?
P(None) is the complement of the union. It measures the chance that none of the three events occur in the same experiment.
7. Are conditional results always defined?
No. A conditional probability needs a positive conditioning event. If the denominator is zero, the calculator marks that conditional value as undefined.
8. What can I do with the exports?
Use CSV for spreadsheets or datasets, and PDF for printable records, class notes, audit evidence, or quick sharing with colleagues.