Mutually Exclusive Events

Definition

Mutually exclusive events are those events which can not occur together. Mutually non-exclusive events are those events which can occur together because they have one or more common outcomes.

Understand By Example

Let us understand mutually exclusive events by an example.

On tossing a number cube, you can get any one of six faces up. Getting 1 on the cube is an event and getting another number, say 4, is another event. We know that a number cube can't show both the faces 1 and 4 at the same time. Thus, only one of the two events 1 or 4 may occur. In other words, if the outcome is 1, you can't get 4 and if the outcome is 4, you can't get 1.

Such events of an experiment, either of which may occur individually but both may not occur together, are called mutually exclusive events, because the occurrence of one event excludes the occurrence of the other.

In the above example, suppose one event is "getting an even number". There are three even numbers on a number cube, 2, 4 and 6. Another event is "getting prime number". There are four prime numbers on a number cube, 1, 2, 3 and 5 (1 is not a prime number but it is not even, so we are assuming it to be prime in this example). Now suppose you toss the coin and get an outcome of 2. 2 is a prime number and an even number as well. In this case, both the events (getting an even number and getting a prime number) have occurred together. Such events which may occur together because they have one or more matching outcomes (such as 2 in this case), are called mutually non-exclusive events.