In the theory of probability, two events are said to be mutually exclusive events if they cannot occur simultaneously or at the same time. Mutually Exclusive events are termed as disjoint events.In simple words, mutually exclusive events are the events or actions which are opposite to each other. Mutually exclusive events are those that can never occur simultaneously according to probability theory. To put it another way, if one event has already happened, another event cannot. As a result, the conditional probability of events that cannot coexist is always zero. Mutually exclusive events cannot occur simultaneously.
Things that are mutually exclusive are not able to occur simultaneously. In business, this is typically concerning the undertaking of projects or allocating a budget. If two things are not mutually exclusive, it means the existence and occurrence of one does not necessarily mean the other cannot coexist. Mutually exclusive events cannot happen at the same time, while independent events have no influence on each other’s occurrence. Mutually exclusive is a statistical term describing two or more events that cannot happen simultaneously.
- Within each suit are 3 face cards – Jack, Queen, and King.
- This brings us to the topic of “mutually exclusive events”.
- Mutually exclusive events cannot happen simultaneously, but should not be considered independent 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.
Are independent events mutually exclusive?
Students will first learn about mutually exclusive events as part of statistics and probability in 7th grade. The events that cannot happen at the same time are termed mutually exclusive events. There are times when it is very important to determine if two events are mutually exclusive or not. Knowing whether two events are mutually exclusive influences the calculation of the probability that one or the other occurs. Now we will conduct the same probability experiment of rolling two dice and adding the numbers shown together.
Bayes’ Theorem – Bayes’ Theorem and Bayesian Inference Unraveling the Mysteries of Probability
The projects, in this case, directly compete with each other. Mutually exclusive events can be depicted using Venn diagrams. Again, we note from the Venn diagram that $E2$ and $E3$ share an overlapping region and hence are NOT mutually exclusive. We note from the Venn diagram that $E1$ and $E3$ do overlap and hence are NOT mutually exclusive. We note from the Venn diagram that $E1$ and $E2$ do not overlap and hence are mutually exclusive. For instance, if we roll a die, then we can either get an even number or an odd number, but it is impossible to have an outcome that is both even and odd.
However, you can roll a five and a three on two dice. 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. Here we will learn about mutually exclusive events, including what they are and how to find the probability of mutually exclusive events occurring.
Real-life Examples on Mutually Exclusive Events
- 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 will discuss events and specifically mutually exclusive events.
- Therefore, “India winning” and “Pakistan winning” are mutually exclusive events, as the occurrence of one excludes the other.
Rolling a five on one and a three on the other means they are not mutually exclusive outcomes. Mutually exclusive events are 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. In a standard deck of 52 cards, there exists 4 kings and 4 aces. Calculated the probability of selecting the letter T or a vowel.
Mutually exclusive events examples
They are referred to as mutually exclusive since neither Set A nor Set B contain any of the elements of the other. Mutually exclusive events are two or more events that cannot occur at the same time. The probability of a face card is therefore the sum of the probabilities of a Jack, a Queen, or a King. Hence, A and B are mutually exclusive and exhaustive. If A ⋃ B be the sample space, then the above two conditions are true. I) On a throw of a die, the two events “getting 1” and “getting 5” are two mutually-exclusive events because we will never get both 1 and 5 at one time in a throw.
Mutually Exclusive Events Solved Examples
Thus, the probability of getting either a even card or a face card is 8/13. Union of SetsThe symbol which defines the union is “∩” it is also called “OR”. We define Union as all the values contained in both sets, i.e. 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 define mutually exclusive events Intersection of the set and the Union of the set.
A and B or (A ⋂ B) is the event of the occurrence of both events A and B. If A and B are two events, then A or B or (A ⋃ B) denotes the event of the occurrence of at least one of the events A or B. 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.
Before, going through this topic will discuss some important term or relations related to it. 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. If you are picking one card, you cannot pick a 9, 10, and a face card at the same time, so the events are mutually exclusive. There are 3 red balls, 7 blue balls, and 5 green balls in a bag.
This is because the money received now can be invested and can generate cash flows, this ultimately leads to future enterprise. The mutual exclusivity concept helps analysts figure out the time value of each option. Mutually exclusive events are events that cannot happen at the same time. In other words, the occurrence of one event excludes the occurrence of the other. If two events are mutually exclusive, the probability of them both occurring simultaneously is zero. 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.
In finance, analysis of disjoint events facilitates crucial decision-making like selecting an investment opportunity or capital budgeting. The time value of money comes into play when one has to choose between mutually exclusive investment options or business projects. Time value of money refers to the concept where money received in the present is of higher worth than money to be received in the future.
Hence, the probability of two mutually exclusive events occurring at the same time is zero. For instance, the result of an exam can either be pass or fail, but never both. 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. Some other real-life examples of mutually exclusive events are, while throwing a die getting any two numbers simultaneously is a mutually exclusive event.
