# MUTUALLY EXCLUSIVE: What It Is, in Business and Examples

A statistical term used to describe events that cannot occur simultaneously is “mutually exclusive.” It is often used to say that one thing is more important than another. This article gives more explanation of mutually exclusive statistics, mutually exclusive probability, and mutually exclusive examples.

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## What is Mutually Exclusive?

Events that cannot occur simultaneously but should not be regarded as independent are those that are mutually exclusive. Independent occurrences have little bearing on whether alternative solutions are viable. Take rolling the dice as a simple illustration. On the same die, you cannot simultaneously roll a three and a five. On two dice, you can definitely roll a five and a three. When you roll both a five and a three, the results are mutually exclusive. If you roll a five on one and a three on the other, the results are not exclusive of one another.

### Opportunity Cost

When deciding between two options that can’t be done at the same time, a business must think about what it would have to give up to go with each one. This is called opportunity cost. The ideas of opportunity cost and mutual exclusivity are inextricably linked because each mutually exclusive choice means giving up any profits that could have been made by choosing the other choice.

The analysis of mutual exclusion is slightly complicated by the time value of money (TVM) and other considerations. Businesses use the net present value (NPV) and internal rate of return (IRR) calculations to figure out which project is more profitable when they have to choose between two or more options that can’t be combined.

## Mutually Exclusive in Statistics

Statistics say that these things can’t happen at the same time, like if a coin landed on both heads and tails at the same time. Learn what a mutually exclusive event is, find some examples or make your own, and then compare it to independent and dependent events.

### What Are Mutually Exclusive Events?

We are exposed to a wide variety of idioms and sayings as we mature. There are a few that are so delightfully simple, while others seem to make a little sense. The adage “You can’t have your cake and eat it, too” may be familiar to you. This proverb is the ideal approach to explaining why two occurrences cannot coexist. The adage alludes to the reality that you cannot simultaneously eat your cake and keep it in front of you. According to statistics, it is impossible to have your cake and eat it.

If two events cannot occur at the same moment, they are said to be mutually exclusive. In other words, if one event occurs, the other event is prevented from occurring. Events that are mutually exclusive are occasionally referred to as “fragmented events.”

### ME Events

Driving a car and obtaining a driver’s license, having power at home and paying your electric bill, working as a programmer, and being computer literate are just a few examples of possibilities that can coexist. A further way to look at it is that two occurrences that are mutually inclusive cannot occur independently. When two occurrences are mutually inclusive, they are dependent in some way.

The probability of the intersection of events A and B are used to express the likelihood that occurrences A and B are disjoint or mutually exclusive. P (A B) = 0 represents the probability of disjoint (or) mutually exclusive events. When two events are mutually exclusive, the specific addition rule is applicable in probability. It claims that the likelihood of either event happening is equal to the likelihood of each event happening individually. The probability of an event A occurring or the likelihood of an event B occurring is stated as P(A) + P(B), if A and B are considered to be occurrences that cannot both occur at the same time.

P(A) = P(A) + P (A U B) (B)

## Why Does It Matter

At times, it’s important to figure out if two things can’t happen at the same time or not. A probability calculation for one of two events depends on whether or not they are mutually exclusive.

Review the card example once more. What is the likelihood of drawing a heart or a king if we only draw one card from a typical 52-card deck?

First, separate these into separate actions. We first calculate the number of hearts in the deck, which comes to 13, and divide that number by the total number of cards to get the likelihood that we have drawn a heart. Accordingly, the likelihood of a heart is 13/52.

We start by tallying the total number of kings, which comes to four, then divide that number by the entire number of cards, which is 52, to determine the likelihood that we have drawn a king. There is a 4/52 chance that we have drawn a king.

Finding the likelihood of drawing a heart or a king is the current challenge. Here is when caution is required. The odds of 13/52 and 4/52 are quite alluring when added together. The two events are not mutually exclusive, hence this is incorrect. In these possibilities, the king of hearts has been counted twice. In order to avoid double counting, we must deduct the 1/52 chance of getting both a king and a heart. Therefore, there is a 16/52 chance that we have drawn a heart or a king.

## Mutually Exclusive Examples

In capital budgeting, the idea of mutual exclusivity is frequently used. Businesses could have to pick among several initiatives that, once completed, will provide value to the organization. Some of these initiatives conflict with each other.

Let’s say a business has a \$50,000 budget for growth initiatives. Projects A and B are incompatible if they are both feasible and cost \$40,000 apiece, whereas Project C only costs \$10,000. The business cannot afford to pursue B if it pursues A, and vice versa. Project C might be seen as being independent. The business can still afford to pursue Project C regardless of the other projects chosen. The feasibility of C is unaffected by the acceptance of either A or B, and the viability of either of the other projects is unaffected by the acceptance of C.

Consider the study of Projects A and B as well when examining opportunity costs. Consider that while Project B will only yield \$80,000, Project A might potentially yield \$100,000. Since options A and B are mutually exclusive, the opportunity cost of choosing B is the difference between the profits made by the most profitable choice (in this case, A) and the chosen option (B), or \$100,000 minus \$80,000, or \$20,000. Option A has zero opportunity cost because it is the most profitable choice.

## What Does It Mean If Projects Are Mutually Exclusive?

Managers and directors frequently have to consider how to allocate resources in the workplace. A company that wants to build both a bridge and a skyscraper might find that it can’t do both because only one of the highly specialized pieces of equipment needed for both projects is available worldwide. This is because the equipment cannot be employed for both projects at the same time. This idea can be made bigger to include budgets, specialized staff, and software platforms that can’t run both Mac and Windows.

## How Do You Show Mutually Exclusive Events?

To depict occurrences that are mutually exclusive, we can use Venn diagrams. Events that are not incompatible with one another are depicted in the same figure, while events that are depicted in different figures are demonstrated to be mutually exclusive. Be aware that events that are mutually exclusive lack any commonality.

## What Is the Difference Between Independent and Mutually Exclusive?

Think about the prior example of war and peace to demonstrate the difference between what is independent and what is mutually exclusive.Think back to the example of war and peace to show the difference between things that can happen on their own and things that can’t happen together. Italy could experience calm as France goes to war. Since these two countries are independent of one another, they might each be at peace with themselves. However, France cannot be at war and at peace at the same time. That makes them mutually exclusive because they are unable to coexist.

## Do Mutually Exclusive Events Add up to 1?

There is no way for two events to happen at once if they are mutually exclusive. The probability of mutually exclusive occurrences combined can never be greater than one. Until and unless the same set of occurrences is similarly exhaustive, it is always smaller than 1. (at least one of them being true). Their combined probability in this instance is one.

## Dependent and Independent Events

When the occurrence of one event alters the likelihood of another, two occurrences are said to be dependent. When the likelihood of one event has no bearing on the likelihood of another, the two events are said to be independent. Two occurrences are not independent if they cannot both occur at the same time. Also, you can’t have two separate occurrences cancel each other out.

## Mutually Exclusive Events Probability Rules

According to the theory of probability, two events are mutually exclusive if they don’t happen at the same time. The outcomes of a single coin flip, which can result in either heads or tails but not both, are an obvious example. When you flip a coin, both outcomes are exhaustive, which means that at least one of the possible outcomes must happen. This means that these two outcomes eliminate all other possibilities.

However, not all events that are ME are necessarily exhaustive. For instance, the outcomes of rolling a six-sided die and getting a 1 and a 4 are mutually exclusive events (a 1 and a 4 cannot come up as the result at the same time), but they are not all possible possibilities (it can result in distinct outcomes such as 2,3,5,6). Further, the following probability laws can be deduced from the notion of mutually exclusive events.

## Conditional Probability for Mutually Exclusive Events

An event A is said to be “probable,” or “conditionally probable,” if and only if another event B has already taken place. The conditional probability of event B provided that event A has occurred is indicated by the formula P(B|A), and it is defined using the following equation for two independent occurrences A and B.

(A B)/P = P(B|A) (A)

## What Does Mutually Exclusive Mean in Finance?

Usually, this entails payments and budgets. If a company has \$200 million to spend, it cannot reinvest in the company while also providing bonuses to top executives. In this instance, those two possibilities are incompatible. If a company can only keep a license in one country, it shouldn’t try to keep licenses in two countries since they can’t work together.

## Does Mutually Exclusive Mean Independent?

A pair of events is said to be ME if they can’t happen at the same time. A pair of events is said to be independent if the happening of one event doesn’t affect the happening of the other.

## Uses of Mutually Exclusive

In reality, the addition rule is used to talk about a few formulas that are almost the same. Before we can figure out which addition formula to use, we need to know if our events are mutually exclusive.

## How Do You Know if It’s Mutually Exclusive?

Statistics say that for two or more events to happen at the same time, they must be mutually exclusive. It is often used to say that one thing is more important than another. For instance, it is impossible for war and peace to exist together. As a result, they are diametrically opposed.

## How Can 3 Events Be Mutually Exclusive?

If at least two events are the same and have the same possible outcomes, then the outcomes of the three events cannot be the same.

## Final thoughts

Mutually exclusive events cannot take place at the same time. In the corporate world, this usually has to do with starting initiatives or setting aside money. When two things do not conflict with one another, it is said that they are not necessarily incompatible with one another.

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