Get the latest information and updates on GPRC’s response to COVID-19
Skip to Main Content
It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results.

Math

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:
                                                             
Grande Prairie Campus
10726 - 106 Avenue
Grande Prairie, AB T8V 4C4
Phone: 1-780-539-2939
Email: library@gprc.ab.ca
Fairview Campus
11235-98 Avenue
Fairview,AB T0H 1L0
Phone: 1-780-835-6750
Email: fvlibrary@gprc.ab.ca