If you’re wondering what mutually exclusive means — keep reading. In this guide, we explore the meaning of mutually exclusive, its origin, and more.
What Does Mutually Exclusive Mean?
The pronunciation looks like: [ myoo-choo-uh-lee ik-skloo-siv, -ziv ]
According to Dictionary.com, “mutually exclusive” is an adjective that describes two or more events, possibilities, etc., that can’t happen simultaneously.
In another definition brought to us by the Collins Dictionary, if two events are mutually exclusive, they are separate and very different from each other, so it is impossible for them to exist or happen together.
Although these definitions vary slightly, we can determine that the term mutually exclusive can be defined as unable to be both true at the same time. For example, you can’t run backward and forwards at the same time — the events “running backward” and “running forward” are mutually exclusive.
A coin toss is another example as you can’t get both heads and tails. So “tossing a heads” and “tossing a tails” are mutually exclusive. By contrast, sunshine and rain are not mutually exclusive; although rare, it is possible to have rain when the sun shines.
The term mutually exclusive first appeared sometime in the 1870s.
How To Calculate Mutually Exclusive Events
So in short, events that are mutually exclusive (called disjoint events) are those that do not occur at the same time.
The occurrence of mutually exclusive events at the same time is 0. In regards to math and statistics, if A and B are two mutually exclusive events, the probability of them both taking place at the same time is: P(A and B) = 0. The formula for calculating the probability of two mutually exclusive events is as follows:
P(A or B) = P(A) + P(B)
When showing the relation between sets, special symbols are used, such as:
- Intersection of sets: “∩”and “and”
- Union of sets: “∪”and “or”
More Examples of Mutual Exclusion
In addition to what we’ve already covered above, here are more examples of mutually exclusive events listed below:
- When reaching a fork in the road, you can either go left or right — this is a mutually exclusive event as you can’t do both at the same time.
- In a regular deck of 52 cards, drawing a red card and drawing a club are mutually exclusive events since all the clubs in a deck are always black.
- In a six-sided die, the events “2′ and “5” are mutually exclusive because getting both events at the same time is impossible.
- When playing with dice, rolling an even and odd number on a single six-sided die is a mutually exclusive event.
- When playing a game, winning and losing are mutually exclusive events.
- Running and walking are mutually exclusive as you can’t run and walk at the same time.
- When deciding whether or not to attend college, the two options are mutually exclusive.
Examples of Non-Mutually Exclusive Events
Here are examples of events that are not mutually exclusive:
- Driving and listening to the radio
- Even numbers and prime numbers on a die
- Losing a game and scoring
- Running and sweating
- Drawing the king of hearts and a red card
Synonyms of the Term Mutually Exclusive
To further your understanding of the term mutually exclusive, it can be helpful to discover words that have the same or nearly the same meaning as mutually exclusive.
These like-words are called synonyms and are listed below:
Antonyms of the Term Mutually Exclusive
In addition to learning synonyms, discovering words that have the opposite meaning of mutually exclusive will sharpen your overall sense of language while strengthening your understanding of the term.
These words are called antonyms and are listed below:
Mutually Exclusive Sentence Examples
Now that you have a pretty good understanding as to what mutually exclusive means, let’s take a look at some examples of the term being used in a sentence:
“Apparently, she didn’t get the memo that style and comfort don’t have to be mutually exclusive.”
“Though the words sound like antonyms, independence and interdependence are not mutually exclusive.”
“From a business standpoint, mutually exclusive scenarios are evaluated in capital budgeting situations.”
“In probability theory, two things are said to be mutually exclusive if they can’t occur at the same time or simultaneously.”
“She said the two approaches don’t have to be mutually exclusive.”
“My friend Ace doesn’t view doing well and doing good as mutually exclusive.”
“The two goals you are suggesting are pretty much mutually exclusive.”
“While not mutually exclusive, the two roles can be incompatible.”
“At the end of the argument, both parties remained committed to their mutually exclusive demands.”
“I don’t care what you say; those two options are not mutually exclusive.”
“When deciding how to invest, a business often has to pick between two mutually exclusive projects.”
“Although it may feel as though losing weight and eating tasty food are mutually exclusive, they aren’t.”
“Project A and Project B are mutually exclusive — we simply can’t do both.”
“She said the event happening on Saturday is mutually exclusive to the inclement weather.”
“Did you know drawing a red card and drawing a club are mutually exclusive, whereas drawing a black card and drawing a spade is not?”
“When trying to decide between two mutually exclusive events, it’s wise to take into account the potential return and the total number of outcomes (including the possible outcomes) for both event A and event B.”
“He didn’t say it was mutually exclusive, but he did say the odds were extremely low, and the probability of such event is highly unlikely.”
“Paying rent and not having a negative bank account often seem mutually exclusive.”
So, what does mutually exclusive mean, you ask?
Simply put, mutually exclusive refers to two things or more that are separate from each other and can’t co-exist. In other words, when two events are mutually exclusive, they can’t happen simultaneously — it’s one or the other.
We hope this guide has provided you with the information needed to fully understand the meaning of mutually exclusive and how to use the term in a sentence. If you ever get confused about the concept of mutual exclusivity, feel free to refer back to this guide for help!