# Mutually Exclusive Events

Some events of a probability experiment can occur simultaneously and some events cannot occur simultaneously.

**For example,** consider the experiment of throwing die. Let us define the event A as getting an odd number and the event B as getting an event number and the third event C as getting a multiple of 3. The outcomes of the three events can be listed as follows:

A = {1, 3, 5} B = {2, 4, 6} and C = {3, 6}

Events A and C have the outcome 3 as common, while B and C have the outcome 6 in common. The events A and B do not share any common outcomes. Suppose the outcome turns out to be 3, we conclude that both the events A and C have occurred. And for the outcome 6, we say that both the events B and C have occurred. But there is no possibility of saying that both the events A and B have occurred. A and B are hence the mutually exclusive events. This against events A and C or the events B and C are not mutually exclusive and hence mutually inclusive events.