Mutually Exclusive Events Calculator
Add the probabilities of mutually exclusive events to get P(A or B) = P(A) + P(B), and check whether the events can be disjoint at all.
How it works
P(A ∪ B) = P(A) + P(B), when P(A ∩ B) = 0
Mutually exclusive (disjoint) events cannot occur at the same time, so there is no overlap to subtract and their union is simply the sum. This only works when the events are truly exclusive — if the two probabilities add to more than one, they must overlap and the simple sum is invalid. For overlapping events you need the general addition rule that subtracts P(A and B).
Worked example
Rolling a die, A = “roll a 2” (P = 1/6) and B = “roll a 5” (P = 1/6) are exclusive, so P(A or B) = 1/6 + 1/6 = 1/3, about 33.33%.
Sources: Mutual exclusivity — Wikipedia
Frequently asked questions
How do I know if events are mutually exclusive?
They are exclusive when they share no outcomes — P(A and B) = 0. Rolling a 2 and rolling a 5 on one die are exclusive; “rolling even” and “rolling a 2” are not.
What if P(A) + P(B) is more than 100%?
Then the events cannot be mutually exclusive — they must overlap. You would use P(A or B) = P(A) + P(B) − P(A and B) instead.
Are mutually exclusive events independent?
No — they are the opposite in a sense. If two events with non-zero probability are exclusive, then one occurring guarantees the other did not, so they are strongly dependent.
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This calculator is for educational purposes. Double-check important results before acting on them.