Mutually Exclusive: Definition, Meaning & Example

KEY TAKEAWAYS

• Mutually exclusive events are events that cannot occur at the same time. 
• The concept often plays a central role in the business world in relation to budgeting and project management.
• The time value of money often plays a key role when talking about mutual exclusivity.

What Is Mutually Exclusive?

Mutually exclusive is a term used in statistics. It is used to describe two or more events that can’t happen at the same time, or simultaneously. It is most commonly used to describe a situation where the occurrence of one situation supersedes another event. 

For example, night and day cannot coexist at the same time. Or you can’t run forward and backward at the same time. This would make these events mutually exclusive.

How Do You Use Mutually Exclusive?

Mutually exclusive can be used whenever there are events that can’t both happen, but shouldn’t be considered events independently from one another. An independent event has no impact on the viability of the other options.

So for example, let’s say you throw a single die. You wouldn’t be able to roll both a six and a two simultaneously on your single die. However, you could easily roll a six and a two on two dice. 

Rolling a six and a two simultaneously on one die means that this outcome is mutually exclusive. Rolling a six and a two on two dice means that they are not mutually exclusive outcomes.

When it comes to business, managers and directors are often put in charge of planning resource allocation. So let’s say a company is expanding its headquarters as well as building a new office in a new location. Now let’s say that both projects require a very specialized piece of equipment and the company can only afford to purchase or rent one of these. 

This would make both the expansion and the new office mutually exclusive. As the specialized piece of equipment cannot be used by both projects at the same time. This idea can then be extended so that it can take specialized professionals or software systems into consideration. 

What Is the Difference Between Mutually Exclusive and Non Mutually Exclusive?

The difference between mutually exclusive and non-mutually exclusive is straightforward.

A mutually exclusive event are events that cannot happen at the same time. You can’t win and lose a game. You can’t run and walk. You can’t look left and right. It’s two separate events that simply cannot co-exist. 

Non-mutually exclusive events are events that can absolutely happen at the same time. You can drive and listen to music. You can roll an even number and a prime number on a die. You can lose a game but score a goal. You can run whilst sweating. 

A mutually exclusive event can make calculating probability a relatively simple task. If either is happening or isn’t happening. Whereas non-mutually exclusive events can make figuring out probabilities a more complex task. 

Example of Mutually Exclusive

Let’s now put mutually exclusive terms in a business sense. 

The concept of using mutual exclusivity is often used in capital budgeting. A company may be in a situation where they have to choose between a number of different projects. These are projects that aim to add value to the company once they’ve been completed. Some of these projects would be mutually exclusive. 

So for example, let’s say that Company X has a budget of $500,000 for expansion projects. 

Let’s say Project A and Project B each cost $400,000. And Project C only costs $100,000. Then both Project A and Project B would have to be considered mutually exclusive. If Company X decides to pursue Project B, then it would not be able to also pursue Project A and vice versa. 

Project C can be considered independent. This is because regardless of which project Company X chooses, it will still be able to afford to pursue Project C as well. Therefore the perusal of Project A or Project B does not impact how viable Project C is. And the perusal of Project C does not impact the viability of either Project A or Project B. 

Opportunity Cost

When a person is faced with a choice between mutually exclusive options, the opportunity cost must be taken into consideration. This is what you would be giving up to pursue each option. 

The concept of opportunity cost and mutual exclusivity are inherently linked. This is because each option would require the sacrifice of whatever the other had to offer. 

The time value of money (TVM) and other such factors can make mutually exclusive analysis slightly more complicated. When diving into a detailed comparison, a company may use the net present value (NPV) and the internal rate of return (IRR). These formulas can be used to determine which project is more beneficial to the company. 

Summary

Anything that is mutually exclusive cannot occur simultaneously. In business, this is a useful tool when considering project management and budget allocation. If the two things are not mutually exclusive, then it means that the existence of one doesn’t impact the existence of the other.