Robinhood Learn

Democratize finance for all. Our writers’ work has appeared in The Wall Street Journal, Forbes, the Chicago Tribune, Quartz, the San Francisco Chronicle, and more.

Definition:

Mutually exclusive refers to the relationship between two or more events that cannot occur at the same time.

## 🤔 Understanding mutual exclusivity

When two events are mutually exclusive, they cannot happen simultaneously — It’s one or the other. The existence of mutually exclusive events results in an inherent opportunity cost, which is the cost of losing out on one of the events that can’t both happen at the same time. Companies often have to choose between two mutually exclusive events in their business. For example, they might have to choose between two capital projects, only one of which they can afford to do at a time. In some cases, the different options are collectively exhaustive, meaning at least one of the events has to occur. Finally, two events could be independent of one another, in which case the occurrence of one does not affect the other.

Example

Imagine that you’re driving down the road, and you’ve arrived at an intersection. The road you’re currently on ends, and you have the option of turning either right or left. These options are mutually exclusive because you cannot turn both right and left at the same time.

## Takeaway

Ready to start investing?

Sign up for Robinhood and get stock on us.

Sign up for Robinhood

Certain limitations apply

New customers need to sign up, get approved, and link their bank account. The cash value of the stock rewards may not be withdrawn for 30 days after the reward is claimed. Stock rewards not claimed within 60 days may expire. See full terms and conditions at rbnhd.co/freestock. Securities trading is offered through Robinhood Financial LLC.

Tell me more…

- What are some mutually exclusive events?
- What does mutually exclusive and exhaustive mean?
- What is the difference between mutually exclusive and independent?
- What is the opportunity cost with mutually exclusive options?

## What are some mutually exclusive events?

Two events are mutually exclusive if they cannot both occur at the same time. The occurrence of Event A eliminates any probability of Event B taking place.

Mutually exclusive events also occur regularly in corporate finance. Companies often use capital budgeting to invest in future business growth. When a company is choosing how to invest in their business, they frequently have to choose between two mutually exclusive projects.

For example, let’s say a company has $500,000 to invest in future growth. The business owner is considering two different projects, both of which would cost about half a million dollars. The two projects are mutually exclusive. Because they would both use all of the working capital the company has set aside to invest, it is only possible for them to complete one of the projects.

The concept of mutual exclusivity could also come into play for hiring decisions. If a company is conducting interviews for a new chief executive officer (CEO), they might narrow it down to two different candidates. The two choices are mutually exclusive — The company cannot hire two CEOs.

## What does mutually exclusive and exhaustive mean?

When two events are mutually exclusive, it means they cannot both occur at the same time. But it doesn’t necessarily imply that one of the two events has to happen.

When two events are exhaustive, it means that one of them must occur.

Think again of a coin toss. The results are mutually exclusive (it will be either heads or tails; it can’t be both on the same flip). And it will be one of the two options — heads and tails are the only possible options (thus they are exhaustive).

## What is the difference between mutually exclusive and independent?

Mutually exclusive events are two events that cannot occur at the same time. The occurrence of one event has a direct impact on the probability of the other. Independent events are the exact opposite — Independent events are those that do not affect the likelihood of each other.

The results of multiple coin flips are independent of one another. We know that when we flip a coin, the chances of flipping either heads or tails are mutually exclusive. We can’t flip both heads and tails at the same time. But what about if you flip a coin three times in a row? The results of the first coin flip and are completely independent of the results of the second and third coin flips. Flipping heads on one of the flips doesn’t make you any more or less likely to flip heads the next time.

The concept of independent events also applies to capital financing. We know that two capital projects are mutually exclusive if the company can only invest in one of them. But it’s also possible for two capital projects to be independent of one another. Let’s say a corporation has a great deal of funding available for capital projects, and they are considering two different options.

In this case, the company could likely invest in both projects if they wanted. Whether they decide to invest in one of the projects has no impact on whether they invest in the other. Suppose a company has $1M set aside for business growth. They are considering two projects, both of which have a price tag of $100,000. If the company invests in Project A, they aren’t necessarily any more or less likely to also invest in Project B.

## What is the opportunity cost with mutually exclusive options?

When an individual or company chooses one of two mutually exclusive opportunities, there is always an opportunity cost. The opportunity cost is the potential return on investment of the opportunity they don’t choose.

An example of when an individual might face an opportunity cost when deciding between two mutually exclusive opportunities is when they’re considering what to do after high school. When determining whether or not to attend college, the two options are mutually exclusive.

For someone who chooses to go to college, they have the opportunity cost of the income they could be making if they had entered the workforce right away. And if you only look at the immediate outcome, skipping college might seem more profitable.

But entering the workforce instead of going to college has an opportunity cost as well. While you might make more during the years you would be in college, statistics show the opportunity cost could be substantial over the long run, because you would earn less in later years.

Imagine that a company is investing in a capital project. They’re weighing two options, but they can online invest in one of them. The first option costs $100,000, and the company expects it will bring in an additional $15,000 of annual revenue for 20 years. The second project will cost $200,000, and the company expects it will bring in $18,000 of annual revenue for 20 years.

For the first project, the total revenue would equal $300,000 ($15,000 x 20), with a total profit of $200,000 (ignoring inflation, costs of capital, etc.). The revenue of the second project would come to $360,000 ($18,000 x 20). The revenue is higher, but because the project was more expensive, the profit margin is lower at $160,000.

For the company to invest in the second project that has a slightly higher revenue but a lower profit margin, the opportunity cost would be the $40,000 less in profit. And the implications are even more significant than that. Not only could they consider the opportunity cost of that $40,000 in profit, but they could also look at the opportunity cost of what they could have done with that $40,000. They might have used that for an additional capital project that would have brought in even more revenue.

Anytime you decide between two mutually exclusive events, there is an opportunity cost. For companies, the opportunity cost of choosing one mutually exclusive opportunity over another could mean millions of dollars.

Ready to start investing?

Sign up for Robinhood and get stock on us.

Sign up for Robinhood

Certain limitations apply

New customers need to sign up, get approved, and link their bank account. The cash value of the stock rewards may not be withdrawn for 30 days after the reward is claimed. Stock rewards not claimed within 60 days may expire. See full terms and conditions at rbnhd.co/freestock. Securities trading is offered through Robinhood Financial LLC.

## Related Articles

## You May Also Like

## FAQs

### What does mutually exclusive mean? ›

Mutually exclusive is **a statistical term describing two or more events that cannot happen simultaneously**. It is commonly used to describe a situation where the occurrence of one outcome supersedes the other.

### What is a mutually exclusive example? ›

In statistics and probability theory, two events are mutually exclusive if they cannot occur at the same time. The simplest example of mutually exclusive events is **a coin toss**. A tossed coin outcome can be either head or tails, but both outcomes cannot occur simultaneously.

### How do you know if it is mutually exclusive? ›

How to find if two events are mutually exclusive? If two events are mutually exclusive then **the probability of both the events occurring at the same time is equal to zero**. P(A and B) = 0.

### What does mutually exclusive mean in math? ›

If two events have no elements in common (Their intersection is the empty set.), the events are called mutually exclusive. Thus, P(A∩B)=0 . This means that the probability of event A and event B happening is zero. They cannot both happen.

### What is mutually exclusive vs independent? ›

The difference between mutually exclusive and independent events is: a mutually exclusive event can simply be defined as a situation when two events cannot occur at same time whereas independent event occurs when one event remains unaffected by the occurrence of the other event.

### What does mutually exclusive mean in law? ›

Mutually exclusive part means that **it can never be the case that two outcomes in the space happen simultaneously**. In other words, during one trial, if you know that one outcome has occurred, then you know that none of the other outcomes have occurred.

### What does mutually exclusive mean in a relationship? ›

An exclusive relationship is where **both partners agree to focus on each other and not see other people**.

### What is mutually exclusive in research? ›

Response options to a survey question are mutually exclusive **when only one response option can be true for a single respondent**.

### What is meant by mutually exclusive events in probability? ›

This is an example of mutually exclusive events. In probability theory, two events are said to be mutually exclusive events if they cannot occur at the same time or simultaneously. In other words, mutually exclusive events are called disjoint events.

### What is opposite of mutually exclusive? ›

**contrary,** **diametric**. **(or diametrical)**, opposing, opposite.

### What is mutually independent? ›

A set of events is said to be mutually independent **if the probability of each event in the set is the same no matter which of the other events has occurred**.

### What is another word for mutually exclusive? ›

incompatible | conflicting |
---|---|

at odds | mutually incompatible |

different | contrary |

opposed | opposite |

differing | antagonistic |

### How do you do mutually exclusive probability? ›

If they are mutually exclusive (they can't occur together), then the (∪)nion of the two events must be the sum of both, i.e. 0.20 + 0.35 = 0.55. In our example, 0.55 does not equal 0.51, so the events are not mutually exclusive.

### Is disjoint and mutually exclusive the same? ›

**Disjoint events are events that never occur at the same time.** **These are also known as mutually exclusive events.**

### What does exclusive mean in math? ›

**Excluding the endpoints of an interval**. For example, "the interval from 1 to 2, exclusive" means the open interval written either (1, 2) or ]1, 2[. See also. Inclusive, interval notation.

### Can 2 events be mutually exclusive and independent? ›

**Yes, there is relationship between mutually exclusive events and independent events.**

### Is mutually exclusive independent or dependent? ›

Suppose two events have a non-zero chance of occurring. Then if the two events are mutually exclusive, they can not be independent. If two events are independent, they cannot be mutually exclusive.

### What is the difference between mutually exclusive and inclusive events? ›

2 events are **mutually exclusive when they cannot both occur simultaneously.** **2 events are mutually inclusive when they can both occur simultaneously**.

### What does mutually exclusive mean Venn diagram? ›

Mutually exclusive means that **A and B cannot both happen at the same time**. Venn Diagram showing mutually exclusive events: The events 'draw an Ace' and 'draw a Heart' are not mutually exclusive as the Ace of Hearts means both events happen together. Venn Diagram showing.

### Does or mean mutually exclusive? ›

**of or relating to a situation involving two or more events, possibilities, etc., in which the occurrence of one precludes the occurrence of the other**: mutually exclusive plans of action.

### What does being mutually mean? ›

If the feeling is mutual, **both of you feel the same the way**, like a mutual admiration society. Mutual means shared. In finance it is used to describe trusts or funds that pool the money of many investors to buy securities. Mutual is a word to describe something two people or groups share.

### Is Exclusive the same as boyfriend girlfriend? ›

"Being exclusive means that you are not seeing anyone else or proactively pursuing another person. **Exclusive means you aren't in a committed relationship just yet, but that doesn't mean that it couldn't eventually turn into one**," Sullivan says.

### Does dating mean boyfriend girlfriend? ›

**Dating is a stage of romantic relationships in which two individuals engage in activity together**, most often with the intention of evaluating each other's suitability as a partner in a future intimate relationship.

### What is inclusive and exclusive? ›

The inclusive 'we' is used if the addressee is included in the reference; it means something like 'you and I (and possibly others)'. In contrast, the exclusive 'we' is used if the addressee is not included in the reference. This form of 'we' means something like 'I and others (not you)'.

### What does it mean to say two things are not mutually exclusive? ›

phrase. If two things are mutually exclusive, they are separate and very different from each other, so that it is impossible for them to exist or happen together. They both have learned that ambition and successful fatherhood can be mutually exclusive.

### What does it mean for three events to be mutually exclusive? ›

Mutually Exclusive: can't happen at the same time. Examples: Turning left and turning right are Mutually Exclusive (you can't do both at the same time) Tossing a coin: Heads and Tails are Mutually Exclusive.

### Is rolling two dice mutually exclusive? ›

Example 2 A pair of dice is rolled. The events of rolling a sum of 6 and of rolling a double have the outcome (3,3) in common. These two events are NOT mutually exclusive.

### What is the meaning of mutually dependent? ›

adjective**unhealthy psychological reliance of one person on another**. addicted.

### What is the opposite of mutually exclusive in statistics? ›

I think "**mutually inclusive**" means things can occur simultaneously (in this sense it's the opposite of "mutually exclusive") but they can also occur independently (i.e. one, or some, and possibly but not necessarily all).

### What is the opposite of mutually? ›

inconsistent | clashing |
---|---|

in disagreement | in opposition |

mutually exclusive | not in harmony |

not in keeping | out of keeping |

out of place | out of step |

### How do you prove mutually independent? ›

Mutual Independence of three events For any three events A, B and C to be mutually independent the following two conditions must be met: **P(A∩B∩C)=P(A)×P(B)×P(C)** A and B must be independent, B and C must be independent and A and C must be independent.

### Why are mutually exclusive events independent? ›

Are mutually exclusive events independent? - YouTube

### How do you know if events are mutually independent? ›

28. Events A and B are independent **if the equation P(A∩B) = P(A) · P(B) holds true**. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.

### What does exclusive of each other mean? ›

adj. 1 **excluding all else; rejecting other considerations, possibilities, events, etc**. an exclusive preoccupation with money.

### What is mutually exclusive events in biology? ›

Two events are mutually exclusive **when they cannot occur at the same time**. In terms of biology, growth and reproduction are mutually inclusive events in unicellular organisms like bacteria. But in higher plants and animals, growth and reproduction are mutually exclusive events as they do not occur together. Regards.

### What is not mutually exclusive in probability? ›

Non-mutually-exclusive means that **some overlap exists between the two events in question** and the formula compensates for this by subtracting the probability of the overlap, P(Y and Z), from the sum of the probabilities of Y and Z.

### What is meant by mutually exhaustive events? ›

What are Mutually Exhaustive Events? **When a sample space S is divided into many mutually exclusive events such that their union forms the entire sample space**, these events are said to be mutually exhaustive events.

### Do mutually exclusive events add up to 1? ›

**The sum of probabilities of two mutually exclusive events will always be 1** . The sum of probabilities of two mutually exclusive events will always be 1 .

### What does mutually disjoint mean? ›

We say that the sets in A are mutually disjoint **if no two of them have any elements in common**. In other words, if A,B∈A, and A≠B, then A∩B=∅.

### Are E1 and E2 mutually exclusive events Why or why not? ›

**E1 and E2 have no elements in common and therefore are mutually exclusive**.

### What is inclusive and exclusive in math? ›

You can remember it easily: **Inclusive - Including the last number**. **Exclusive - Excluding the last number**.

### What does it mean to be in a mutually exclusive relationship? ›

An exclusive relationship is all about being monogamous — meaning, **you're exclusively committed to one person**. You've been dating someone awesome, spending all of your time together, and you realize you don't want to see anyone else. You're ready to make it exclusive!

### What does mutually exclusive mean in research? ›

First, the categories (response options) must be mutually exclusive, which means **they do not overlap with one another**. Second, survey response options must be collectively exhaustive, meaning they provide all possible options that could comprise a response list.

### What does mutually exclusive mean Venn diagram? ›

Mutually exclusive means that **A and B cannot both happen at the same time**. Venn Diagram showing mutually exclusive events: The events 'draw an Ace' and 'draw a Heart' are not mutually exclusive as the Ace of Hearts means both events happen together. Venn Diagram showing.

### What's another word for mutually exclusive? ›

incompatible | conflicting |
---|---|

irreconcilable | antithetical |

disjoint | at variance |

at odds | mutually incompatible |

different | contrary |

### What is mutually exclusive and inclusive? ›

Mutually exclusive events. 2 events are mutually exclusive when they cannot both occur simultaneously. Mutually inclusive events. 2 events are mutually inclusive when they can both occur simultaneously.

### Is Exclusive the same as boyfriend girlfriend? ›

"Being exclusive means that you are not seeing anyone else or proactively pursuing another person. **Exclusive means you aren't in a committed relationship just yet, but that doesn't mean that it couldn't eventually turn into one**," Sullivan says.

### Does dating mean boyfriend girlfriend? ›

**Dating is a stage of romantic relationships in which two individuals engage in activity together**, most often with the intention of evaluating each other's suitability as a partner in a future intimate relationship.

### What's the opposite of mutually exclusive? ›

**contrary,** **diametric**. **(or diametrical)**, opposing, opposite.

### Is disjoint and mutually exclusive the same? ›

**Disjoint events are events that never occur at the same time.** **These are also known as mutually exclusive events.**

### Does or mean mutually exclusive? ›

**of or relating to a situation involving two or more events, possibilities, etc., in which the occurrence of one precludes the occurrence of the other**: mutually exclusive plans of action.

### Are events B and C mutually exclusive? ›

**B and C are mutually exclusive**. (B and C have no members in common because you cannot have all tails and all heads at the same time.)

### What does it mean for three events to be mutually exclusive? ›

Mutually Exclusive: can't happen at the same time. Examples: Turning left and turning right are Mutually Exclusive (you can't do both at the same time) Tossing a coin: Heads and Tails are Mutually Exclusive.

### Are mutually exclusive events independent or dependent? ›

Mutually exclusive events cannot happen at the same time. For example: when tossing a coin, the result can either be heads or tails but cannot be both. Events are independent if the occurrence of one event does not influence (and is not influenced by) the occurrence of the other(s).

### What is the meaning of mutually dependent? ›

adjective**unhealthy psychological reliance of one person on another**. addicted.

### What's the opposite of exclusive? ›

The opposite of exclusive is **inclusive**, and the two terms are often used in discussions of how organizations and groups can be less exclusive and more inclusive.

### What does exclusive of each other mean? ›

adj. 1 **excluding all else; rejecting other considerations, possibilities, events, etc**. an exclusive preoccupation with money.