In this lesson, you will explore probability with both mutually exclusive and non-mutually exclusive events. To do this, you must first be able to classify an event as mutually exclusive or non-mutually exclusive. The easiest way to differentiate between them is to look at examples that are in each category. Recall from the Warm Up that mutually exclusive events cannot occur at the same time, but non-mutually exclusive events can.
Examples of mutually exclusive events :
- Rolling a 2 or 5 on a die.
- Wearing a solid blue T-shirt or wearing a solid red T-shirt. (This assumes you wear only one at a time!)
- Buying a new vehicle that is a van or a truck.
The events in each example cannot occur at the same time.
Examples of non-mutually exclusive events :
- Rolling a number that is greater than 3 or an even number on a die.
- Selecting the answer A on a multiple-choice exam or selecting the correct answer.
- Eating pizza that has ham as a topping or eating pizza that has pepperoni as a topping.
In each example, both events can occur at the same time.
A Venn diagram is an excellent tool to represent both mutually exclusive and non-mutually exclusive events. By looking at the Venn diagram for each, you can see clearly the distinction between them.
Recall from Unit 1 that the rectangle in a Venn diagram contains all the outcomes that form the sample space of a particular experiment. It represents the universal set, U .
The circles labelled A and B contain the outcomes of event A and event B . Because the two circles do not overlap, no outcomes are common to both events.