Mutually Exclusive Events Addition Rule

Quick answer: Mutually exclusive events cannot occur together, so P(A ∪ B) = P(A) + P(B). In general subtract the overlap: P(A ∪ B) = P(A) + P(B) − P(A ∩ B).

Worked example

On one fair die roll, find the probability of a 1 or a 6.

1. These outcomes cannot occur on the same roll.
2. P(1) = 1/6 and P(6) = 1/6.
3. Add to obtain 2/6 = 1/3.

Check the result

The favourable set is {1,6}, two of six equally likely outcomes.

Common mistake to avoid

Even and greater-than-3 are not mutually exclusive: 4 and 6 belong to both, so simply adding their probabilities double-counts.

Try it yourself

1. Find P(2 or 3 or 5) on one die. 2. Find P(even or greater than 3).

Answers and reasoning

1. Three distinct outcomes give 3/6 = 1/2. 2. Union {2,4,5,6} gives 4/6 = 2/3, also 3/6 + 3/6 − 2/6.

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