Probability of compound events

or using set notation:

In this case the two intersecting sets A and B represent the events A and B and the universal set represents the sample space S. This is shown in the Venn diagram.

Proof

If and then

If an event A can occur or an event B can occur but A and B cannot both occur, then the two events A and B are said to be mutually exclusive.

In this case .

We can see this from the Venn diagram, where there is no overlap between the sets.

For mutually exclusive events .

If two events A and B are such that where S is the total probability space, then and the events A and B are said to be exhaustive.