Two events are mutually exclusive if they have no outcomes in common.

This means that if event \(A\) happens, then event \(B\) cannot happen at the same time.

For mutually exclusive events \(A\) and \(B\):

We can add the probabilities directly because there is no overlap.

One fair die is rolled.

Let:

• \(A\): getting a 2
• \(B\): getting a 5

These events are mutually exclusive because a die cannot show 2 and 5 at the same time.

\[ P(A)=\frac{1}{6}, \qquad P(B)=\frac{1}{6} \]

So:

If two events can happen together, then they are not mutually exclusive.

In that case, we must subtract the overlap:

This avoids counting the common outcomes twice.