Mutually exclusive events

When talking about probability, if two events are mutually exclusive, it means that both can’t happen. Only one of them.

For example, if we roll a die, the events “rolling a 1” and “rolling a 2” are mutually exclusive. If we roll a 1, we can’t also roll a 2.

On the other hand, “rolling an even nuumber” and “rolling a prime number” are not mutually exclusive, because we can roll a 2, which is both even and prime.

If we draw this as a venn diagram, mutually exclusive events would be two circles that don’t overlap.

If A and B are mutually exclusive events, A and B cannot both occur at the same time.

Probability of mutually exclusive events both happening

Given that the two events can’t happen at the same time, we can write this probability:

P(A \cap B) = 0