The probability union is the chance of two or more events occurring whether they are mutually exclusive or not. Events are mutually exclusive when there is no crossover between all the different possibilities, and if so, then the addition rule can be used to find the probability union. However, if the events are not mutually exclusive, then the intersection, or common ground, needs to be removed.
If two events are mutually exclusive, then the probability of one of them happening can be calculated by adding together the probabilities for each event. For example, when rolling a die, the chance of getting a 5 or greater is 2 out of 6 possibilities, and the chance of getting a 2 or lower is also 2 out of 6. The probability for these two events adds up to 4 out of 6, which equals a two-thirds chance of the union occurring.
However, if two events are not mutually exclusive, then the probability of the intersection needs to be subtracted from the equation. The reason is that double-counting some events results in a higher probability union than is actually the case. This is usually represented by two ovals, and the area where the two crossover is the common ground between the events.