Overlapping translucent disks beside two distinct selection cards. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
“A or B” normally includes the overlap
In probability notation, the union A or B includes A alone, B alone and both events together. Exactly one of A and B excludes the overlap. These event definitions differ whenever the joint probability is positive, so a calculator should label the requested region rather than rely on the everyday ambiguity of “or.”
Calculate both from one feasible example
Let P(A) = 40%, P(B) = 50% and P(A and B) = 20%. Inclusive OR is 0.4+0.5−0.2 = 0.7, or 70%. Exactly one is 0.4+0.5−2×0.2 = 0.5, or 50%. The A-only region is 20%, B-only is 30%, both is 20% and neither is 30%.
| Event | Included regions | Probability |
|---|---|---|
| At least one | A only, B only, both | 70% |
| Exactly one | A only, B only | 50% |
Use complements at the correct event level
The complement of at least one is neither. The complement of exactly one includes both and neither. Confusing these complements can produce a result that still lies between zero and one but answers the wrong question.
State the relationship rather than assume it
The Probability Calculator offers independent, mutually exclusive and known-intersection models. The example above also happens to satisfy independence, but the region formulas apply to any feasible joint table. Read the feasibility guide before combining separately sourced marginal rates. For a conditional probability after learning B occurred, use the Conditional Probability Calculator; conditioning is a different operation from choosing a union region.
Check the model behind your result
Use the Probability Calculator for the supported calculation and review its stated assumptions before interpreting the output. Find related tools in the Statistics category, or browse the GreenCalc homepage for other calculation topics.
By GreenCalc Editorial Team · Updated 2026-10-26