Calculator Inputs
Use decimal like 0.42, percentage like 42%, or fraction like 21/50.
Example Data Table
| Scenario | P(A) | P(B) | P(A ∩ B) | P(A ∪ B) | Exactly One | Neither |
|---|---|---|---|---|---|---|
| Survey response overlap | 0.45 | 0.35 | 0.15 | 0.65 | 0.50 | 0.35 |
| Mutually exclusive outcomes | 0.20 | 0.30 | 0.00 | 0.50 | 0.50 | 0.50 |
| Event recovery from union | 0.40 | 0.35 | 0.10 | 0.65 | 0.55 | 0.35 |
Formula Used
Main additive rule
For two events, the union probability equals the first event plus the second event minus the overlap: P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Find the overlap
P(A ∩ B) = P(A) + P(B) − P(A ∪ B)
Find Event B
P(B) = P(A ∪ B) − P(A) + P(A ∩ B)
Find Event A
P(A) = P(A ∪ B) − P(B) + P(A ∩ B)
Mutually exclusive case
P(A ∩ B) = 0, so P(A ∪ B) = P(A) + P(B)
How to Use This Calculator
- Select the calculation mode that matches your problem.
- Rename Event A and Event B if you want custom labels.
- Enter known values using decimals, percentages, or fractions.
- Tick the mutual exclusivity box only when both events cannot happen together.
- Press Calculate to show results above the form.
- Review the summary cards, exact-one result, neither result, and conditional probabilities.
- Use the export buttons to download the current results as CSV or PDF.
Frequently Asked Questions
1) What does additive probability measure?
It measures the chance that at least one of two events occurs. The rule adds both event probabilities, then removes shared overlap counted twice.
2) When should I subtract the intersection?
Subtract the intersection whenever both events can happen together. Without subtraction, the shared region is counted once in each event total.
3) What changes for mutually exclusive events?
Mutually exclusive events never occur together, so their intersection is zero. In that case, the union is simply the sum of both probabilities.
4) Can I enter percentages and fractions?
Yes. The calculator accepts decimals like 0.32, percentages like 32%, and fractions like 8/25. It converts everything to probabilities automatically.
5) What does “exactly one event” mean?
It means A happens without B, or B happens without A. Numerically, it equals P(A) + P(B) − 2P(A ∩ B).
6) Why is “neither” displayed?
Neither is the complement of the union. It shows the chance that neither event occurs, so it equals 1 − P(A ∪ B).
7) How can I tell whether my inputs are valid?
Every probability must remain between 0 and 1. The overlap cannot exceed either event, and the union cannot be smaller than one event.
8) Does this calculator check independence?
Yes. It compares P(A ∩ B) with P(A) × P(B). Close agreement suggests independence, while noticeable differences suggest dependence.