### 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**.

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