# Mutually Exclusive: What It Means, With Examples

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. 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. 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.

If we get an even number of Heads then we cannot get an even number of Tails and vice versa. Such events are examples of mutually exclusive events. If two things are mutually exclusive, it means that they cannot co-exist at the same time. In statistics and probability, we use the term mutually exclusive events to define such events that cannot take place together. When two events are mutually exclusive, it means they cannot both occur at the same time.

The outcome of the first roll does not change the probability for the outcome of the second roll. To show two events are independent, you must show only one of the above conditions. If two events are not independent, then we say that they are dependent events. Two mutually exclusive events are events that can not occur simultaneously.

• And, even if one of them occurs, say, inflation, then further events such as lower interest rates and an increase in the value of the dollar can not take place at the same time.
• You can not expect heads and tails in a single flip or event.
• For example, when a coin is tossed then the result will be either head or tail, but we cannot get both the results.
• The two choices are mutually exclusive — The company cannot hire two CEOs.

We also studied the conditional probability of mutually exclusive events. This article also gives the solved examples of mutually exclusive events for better understanding the concept. The concept of independent events also applies to capital financing.

But it doesn’t necessarily imply that one of the two events has to happen. If a card is drawn from a deck, use the addition rule to find the probability of obtaining an ace or a heart. Determine whether the pair of events given below is mutually exclusive.

## The Meaning of Mutually Exclusive in Statistics

It is commonly used to describe a situation where the occurrence of one outcome supersedes the other. We can use Venn diagrams to show mutually exclusive events. The figures shown below indicate mutually exclusive events and events that are not mutually exclusive events or non-mutually exclusive https://1investing.in/ events. Note that there is no common element in mutually exclusive events. There are two paths; one that takes him to school and the other one that takes him home. There are 13 cards in each suit consisting of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king) of that suit.

Mutually exclusive refers to the relationship between two or more events that cannot occur at the same time. Finding the probability of E \(\cup\) F, is the same as finding the probability that E will happen, or F will happen, or both will happen. We will now consider problems that involve the union of two events. To illustrate the difference between what is independent and what is mutually exclusive, consider the war and peace example from earlier. These are two independent nations and therefore each one could be in its own state of peace. However, there cannot be war in France and peace in France.

Such events are frequently encountered during the decision-making process in corporate finance. For example, capital budgeting processes consider mutually exclusive long-term investment projects. You can not expect heads and tails in a single flip or event. Similarly, there are mutually exclusive events in the financial market trading practice.

• We define Intersection as the values that are contained in both sets, i.e.
• As per the definition of mutually exclusive events, selecting an ace and selecting a king from a well-shuffled deck of 52 cards are termed mutually exclusive events.
• Independent projects are those with no effect on the cash flow of other projects being analyzed.
• The sample space S, the events E and F, and E \(\cap\) F are listed below.

When you toss a coin, you either get heads or tails, but there is no other way you could get both results. 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.

## Difference between mutually exclusive and independent events

So B & C and A & B are mutually exclusive since they have nothing in their intersection. Here, we define ∩ the symbol as the intersection of the set and the U symbol as the union of the set. Before proceeding further let’s learn about the Intersection of the set and the Union of the set. The set of all points in the plane that are a fixed distance (the radius) from a fixed point (the centre) is called a circle….

## Real-life Examples on Mutually Exclusive Events

In the last chapter, we learned to find the union, intersection, and complement of a set. We will now use these set operations to describe events. If a company has \$180 million to spend, it cannot spend that \$180 million both by reinvesting in the business and offering bonuses to upper management. In this case, those two options are mutually exclusive. If the company can only retain licensing in a single country, that means they should not attempt to be licensed in two separate countries as they are mutually exclusive. In business, managers and directors often need to plan resource allocation.

Of particular interest to us are the events whose outcomes do not overlap. When faced with a choice between mutually exclusive options, a company must consider the opportunity cost, which is what the company would be giving up to pursue each option. Draw two cards from a standard 52-card deck with replacement. Find the probability of getting at least one black card. Mutually exclusive events are events that can not occur simultaneously, i.e. As these projects were mutually exclusive, the training center was discarded and will be submitted for review again next year.

## Mutually Exclusive Events Formula

Such qualitative data can also be used for dependent variables. For example, a researcher might want to predict whether someone gets arrested or not, using family income or race, as explanatory variables. Here the variable to be explained is a dummy variable that equals 0 if the observed subject does not get arrested and equals 1 if the subject does get arrested. In such a situation, ordinary least squares (the basic regression technique) is widely seen as inadequate; instead probit regression or logistic regression is used. Further, sometimes there are three or more categories for the dependent variable — for example, no charges, charges, and death sentences.

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

Ii) Getting a head or a tail are two mutually-exclusive events. The probability of one or other events is equal to the sum of their separate probabilities. Mutually exclusive events may restrict one from investing in two places at the same time but they also help one decide how to diversify the investments for favourable outcomes. A collection of events is said to be mutually exclusive if only one of those events can take place at a time in a given experiment.

This time we will consider the event consisting of having an odd sum and the event consisting of having a sum greater than nine. Hence \$E2\$ and \$E3\$ are not mutually exclusive events. Hence \$E1\$ and \$E2\$ are not mutually exclusive events. 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.

## Mutually Exclusive Events: Formula, Examples, Calculation, and More

This is because there is a card (the king of hearts) that shows up in both of these events. 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).

In addition, mutually exclusive events can be found in investment management. For instance, due to certain constraints, the portfolio manager may face limited investment opportunities. If some of the opportunities cannot be employed together, they are recognized as mutually exclusive. There can be some mutually exclusive events in the economy such as inflation and deflation.