OR Probability Calculator

Use the addition rule: P(A∪B) = P(A) + P(B) − P(A∩B). You add the individual probabilities and subtract the overlap to avoid double-counting. If the events are mutually exclusive, P(A∩B) = 0, so P(A∪B) = P(A) + P(B).

In probability, OR means 'at least one of the events occurs.' It includes the case where A happens, B happens, or both happen simultaneously. This is formally called the union of events, written as P(A∪B).

Independent events do not affect each other — the occurrence of one has no bearing on the other, and P(A∩B) = P(A) × P(B). Mutually exclusive events cannot both occur at the same time, so P(A∩B) = 0. Note that mutually exclusive events (with non-zero probabilities) are never independent.

When A and B cannot both occur, P(A∩B) = 0, so the formula simplifies to P(A∪B) = P(A) + P(B). For example, rolling a 1 OR a 6 on a single die gives P = 1/6 + 1/6 = 1/3 ≈ 0.333.

Getting a 1 and getting a 6 are mutually exclusive events on a fair die. Each has probability 1/6 ≈ 0.167. Since they can't both happen at once, P(1 or 6) = 1/6 + 1/6 = 2/6 ≈ 0.333 or about 33.3%.

In a Venn diagram, two overlapping circles represent events A and B. The OR probability P(A∪B) corresponds to the total shaded area covered by both circles combined, including the overlap. The AND probability P(A∩B) is just the overlapping region in the center.

No. Probabilities are always between 0 and 1. If you get a result greater than 1, it means your inputs are inconsistent — for example, P(A∩B) must always be less than or equal to both P(A) and P(B), and P(A) + P(B) − P(A∩B) must not exceed 1.

P(exactly one) is the probability that either A or B occurs but NOT both. It equals P(A∪B) − P(A∩B), or equivalently P(A)×(1−P(B)) + P(B)×(1−P(A)). OR probability includes the case where both occur; 'exactly one' excludes that overlap.