Mutually Exclusive Events

Mutually Exclusive Events

Mutually exclusive events are events that cannot happen at the same time. If one occurs, the other cannot occur in the same trial. This matters when finding probabilities for a combined event such as A or B.

Key idea

For mutually exclusive events:

[ P(A \text{ or } B)=P(A)+P(B) ]

There is no overlap to subtract, because the events cannot both happen.

Method

1. Identify the events in the problem.
2. Check whether they can happen together. If they cannot, they are mutually exclusive.
3. Add the probabilities of the two events.
4. Simplify the result if needed.

Important check

Make sure the question really involves mutually exclusive events. If the events can happen together, you cannot simply add the probabilities without adjusting for overlap.

Example check

If event A has probability (\frac{2}{5}) and event B has probability (\frac{1}{5}), and they are mutually exclusive, then

[ P(A \text{ or } B)=\frac{2}{5}+\frac{1}{5}=\frac{3}{5} ]

Always verify that your final answer is in simplest form.