Addition Rule for Mutually Exclusive Events

Addition Rule for Mutually Exclusive Events

When two events are mutually exclusive, they cannot happen at the same time. That means the overlap is zero:

[ P(A \cap B)=0 ]

So the probability that A or B happens is found by adding their probabilities:

[ P(A \cup B)=P(A)+P(B) ]

Method

1. Identify the events in the statement.
2. Check that they are mutually exclusive: if one happens, the other cannot happen at the same time.
3. Add the probabilities of the two events.
4. Simplify the result if needed.

Example structure

If you are given two separate probabilities for disjoint outcomes, compute:

[ P(A \cup B)=P(A)+P(B) ]

Do not multiply, and do not subtract an overlap, because there is none.

Check your answer

• The result should be between 0 and 1.
• If the events are truly mutually exclusive, there should be no double counting.
• If the answer is a fraction, decimal, or percentage, make sure it is fully simplified.

This rule is especially useful for “either/or” situations where the two outcomes cannot occur together.