If two events are **mutually exclusive**, it means that they cannot occur at the same time. For example, the two possible outcomes of a coin flip are mutually exclusive; when you flip a coin, it cannot land both heads and tails simultaneously.

By contrast, rain and sunshine are not mutually exclusive; while rare, it is possible to have a sunshower, when it rains while the sun still shines.

## Examples with playing cards

Let’s look at a few examples of mutual exclusivity involving playing cards. If we have a single standard deck of 52 cards, which of the following pairs of events are mutually exclusive?

A) **Drawing a red card** or **drawing a king**

B) **Drawing a red card** or **drawing a club**

C) **Drawing a black card** or **drawing a spade**

D) **Drawing a black card** or **drawing an ace**

The correct answer is **B)**. Drawing a red card and drawing a club cannot occur at the same time, because all clubs are black; therefore, the outcomes drawing a red card and **drawing a club** are **mutually exclusive**.

The other scenarios are *not* mutually exclusive, because the two characteristics listed can occur together.

For a more formal treatment of mutual exclusivity involving set theory and more involved practice problems, check out this page from the University of California at Berkeley. Otherwise, continue on for a few more examples!

## Mutually exclusive events with a standard 6-sided die

Now that we have a framework for mutually exclusive events, let’s try a few more examples, this time with a standard 6-sided die. Let’s imagine we are rolling this die just once. Can you identify the following pairs of events as mutually exclusive or non-mutually exclusive?

1) **Rolling a number divisible by 2** or **rolling a number divisible by 3**

2) **Rolling a number divisible by 2** or **rolling a number that is a multiple of 5**

3) **Rolling a prime number** or **rolling an even number**

4) **Rolling a non-prime number** **or rolling an odd number**

**Answers:**

1) Non-mutually exclusive (you could a roll a 6, which is divisible by both 2 and 3)

2) Mutually exclusive (you cannot roll a 2,4, or 6 at the same time as you roll a 5)

3) Non-mutually exclusive (you could roll a 2, which is an even prime number)

4) Mutually exclusive (the only non-prime numbers on the die are 4 and 6, which are not odd)

Need more practice identifying mutually exclusive events? Check out our statistics lessons and videos!

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