How do I find the probability of A OR B?
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). See also our Power Set Calculator.
What does 'OR' mean in probability?
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).
What is the difference between independent and mutually exclusive events?
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.
How do I calculate the OR probability of two mutually exclusive events?
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. You might also find our Dice Probability Calculator useful.
What is the probability of obtaining 1 OR 6 in a single die toss?
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%.
How do I represent OR probability in a Venn diagram?
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.
Can the OR probability be greater than 1?
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.
What is 'exactly one' probability and how is it different from OR?
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.