In other words, the probability of the events happening at the same time is zero. From the definition of mutually exclusive events, certain rules for probability are concluded. Two mutually exclusive events are always independent in nature. If one event happens, it affects the probability of happening of the other event. Now, the probability of mutually exclusive events can add up to 1 only if the events are exhaustive, i.e. at least one of the events is true. A capital budget is the evaluation of multiple investment opportunities with the goal of picking the most profitable and value-maximizing options.

- Typically, a look back period of 14 days is considered for its calculation and can be changed to fit the characteristics of a particular asset or trading style.
- Here, we define ∩ the symbol as the intersection of the set and the U symbol as the union of the set.
- The reason why is evident when we examine the outcomes of the events.
- Suppose we draw a card from a standard deck of 52 cards.

It is possible to evaluate independent projects or mutually exclusive projects. Independent projects are those with no effect on the cash flow of other projects being analyzed. These options should be accepted if their net present value is equal or higher than zero. Before, going through this topic will discuss some important term or relations related to it.

## Q2: What are examples of Mutually Exclusive Events?

Conditional probability is stated as the probability of event A, given that another event B has occurred. In statistics, mutually exclusive scenarios are identified as events that can’t happen at the same time. The probability for event Y to happen if event X occurs will always be zero. From a business standpoint, mutually exclusive scenarios are evaluated in capital budgeting situations. It is also important to distinguish between independent and mutually exclusive events.

We can understand it as suppose we have a box containing 5 red balls and 5 blue balls then if we draw a ball it can either be red or blue but can never be both. Thus, these are mutually exclusive events but, if we number each ball from 1 to 5 respectively and then draw a ball and look for either an even-numbered ball or red color. Now in this case it can occur that the ball is even-numbered and red in colour and thus it is a non-mutually exclusive event. In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both. Mutually exclusive events are events that can’t both happen, but should not be considered independent events.

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. For example, assume a company has a budget of $50,000 for expansion projects.

- The term pairwise mutually exclusive always means that two of them cannot be true simultaneously.
- Some other real-life examples of mutually exclusive events are, while throwing a die getting any two numbers simultaneously is a mutually exclusive event.
- You cannot roll both a five and a three simultaneously on a single die.

In statistics and probability theory, two events are mutually exclusive events if they cannot occur at the same time. 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.

Since the events cannot occur simultaneously, their joint probability is always zero. To find the probability that we have drawn a king we start by counting the total number of kings, resulting in four, and next divide by the total number of cards, which is 52. Now we will conduct the same probability experiment of rolling two dice and adding the numbers shown together.

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. The sample space S, the events E and F, and E \(\cap\) F are listed below. Determine whether the following pair of events are mutually exclusive. Next we’ll determine whether a given pair of events are mutually exclusive.

## What Does Mutually Exclusive Mean in Finance?

These events are dependent, and this is sampling without replacement; b. Because you put each card back before picking the next one, the deck never changes. These events are independent, so this is sampling with replacement.

## Calculating mutually exclusive events

Flipping heads on one of the flips doesn’t make you any more or less likely to flip heads the next time. 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. 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. Two events are mutually exclusive if they cannot both occur at the same time.

## What are mutually exclusive events?

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.

This idea can be extended to consider specialized professionals, software systems (which cannot run both Mac and Windows), and allocated budgets. The time value of money (TVM) and other factors make mutually exclusive analysis a bit more complicated. In a box there are three red cards and five blue cards. https://1investing.in/ The red cards are marked with the numbers 1, 2, and 3, and the blue cards are marked with the numbers 1, 2, 3, 4, and 5. You reach into the box (you cannot see into it) and draw one card. Simple events which only have one [possible outcome are always mutually exclusive to other simple events.

If you have any doubts or queries regarding this topic, feel free to ask us in the comment section and we will be more than happy to assist you. We can not worry, and we can not feel happy at the same time. The occurrence of one event prevents the occurrence of another event. So, the events of worry and happiness are mutually exclusive events. For example, turning towards the left and towards the right cannot happen at the same time; they are known as mutually exclusive events. In this article, we will discuss events and specifically mutually exclusive events.

The reason why is evident when we examine the outcomes of the events. Since 11 is in both of these, the events are not mutually exclusive. Imagine that a company is investing in a capital project.

Independent events are those which do not depend on one another, while mutually exclusive events cannot occur together at one time. In this article, we have studied the definition of mutually exclusive events, which tells that two mutually exclusive events cannot occur at the same time. We studied the different examples of mutually exclusive events. When a dice is rolled, we cannot get the numbers \(2\) and \(5\) at the same time. Thus, the events of getting numbers \(2\) and \(5\) on a die are mutually exclusive events. Now, in the case of mutually exclusive events, the probability of one of the events (one or more mutually exclusive events) occurring can be found out.

Since they cannot coexist, that makes them mutually exclusive. In logic, two mutually exclusive propositions are propositions that logically cannot be true in the same sense at the same time. To say that more than two propositions are mutually exclusive, depending on the context, means that one cannot be true if the other one is true, or at least one of them cannot be true. The term pairwise mutually exclusive always means that two of them cannot be true simultaneously. Now let’s see what happens when events are not Mutually Exclusive.

For calculating mutually exclusive events, probability can be used. Probability is considered the most commonly used practice in various fields such as finance, artificial intelligence, game theory, philosophy, etc. A formula known as the addition rule gives an alternate way to solve a problem such as the one above. The addition rule actually refers to a couple of formulas that are closely related to one another. We must know if our events are mutually exclusive in order to know which addition formula is appropriate to use.