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**Mutually Exclusive and Non-mutually Exclusive Events**

Two events are called **mutually exclusive** if they can not happen at the same time. In other words, two mutually exclusive events do not intersect. For example, when we toss a coin, the possible outcomes are a head or a tail. Since these outcomes can not happen at the same time, they are mutually exclusive.

**Example: **In an experiment, we roll a fair die. Event A is rolling an even number and event B is rolling an odd number. Are these events mutually exclusive? Represent these events on a Venn diagram.

##### The sample space is: . The two events A and B are and Since these events do not intersect, they are mutually exclusive. The Venn diagram for this problem is:

##### Two mutually exclusive events A and B satisfy:

##### Two events A and B are called **non-mutually exclusive** if their intersection is not zero. In other words, two non-mutually exclusive events can happen at the same time.

**Example: **In an experiment we roll a fair die. Suppose that event A is rolling an even number and event B is rolling a multiple of 3. Determine whether A and B are mutually exclusive.

##### Events A and B are: , We have:

##### Since A and B intersect, they are non-mutually exclusive. Here is the Venn diagram:

##### Two non-mutually exclusive events satisfy: