# What is the difference between events that are mutually exclusive and those that are not mutually exclusive?

##### 1 Answer

Any *event* can be viewed as a combination of certain *elementary events*. Thus, an event of rolling a dice on an even number is, actually, a set of three elementary events - rolling numbers 2, 4 and 6.

Now, if two *events* are considered, each representing a subset of a set of all possible *elementary events*, they might or might not have certain number of *elementary events* in common. If they don't, these two *events* are called *mutually exclusive*. If they do, they are *not mutually exclusive*.

An example of *mutually exclusive* events are **The dice is rolled on even number** and **The dice is rolled on odd number**.

Obviously, there is no *elementary event* that simultaneously belongs to *events*

An example of *not mutually exclusive* events are **The dice is rolled on even number** and **The dice is rolled on a number greater than 3**.

Obviously, the *elementary events* **The dice is rolled on number 4** and **The dice is rolled on number 6** belong to both *events*