Independent events have no impact on the viability of other options. You cannot roll both a five and a three simultaneously on a single die. However, you absolutely can roll a five and a three on two dice. Rolling a five and three simultaneously means this outcome is mutually exclusive. Rolling a five on one and a three on the other means they are not mutually exclusive outcomes.

We can say that if A and b are two mutually exclusive events then the intersection of their probability is 0. In probability, we define mutually exclusive events as events that can not occur simultaneously. That is if one event happens then it is impossible for another event to happen.

- Independent events are those which do not depend on one another, while mutually exclusive events cannot occur together at one time.
- 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.
- For example, turning towards the left and towards the right cannot happen at the same time; they are known as mutually exclusive events.

A company that manufactures wallets for men is currently evaluating all its investment opportunities for the coming year. The company has three options to invest its resources. The first option is to increase its plant installed capacity, to meet an increasing demand. 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.

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Mutually exclusive events are commonly confused with independent events. Unlike mutually exclusive events, independent events can occur simultaneously. The independence of the events indicates that the outcome probability of one event does not influence the outcome probability of another event. In probability theory, two events are said to be mutually exclusive if they cannot occur at the same time or simultaneously. If two events are considered disjoint events, then the probability of both events occurring at the same time will be zero. Two events are said to be mutually exclusive if they can’t occur simultaneously.

## Not Mutually Exclusive

Information is from sources deemed reliable on the date of publication, but Robinhood does not guarantee its accuracy. 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.

We note from the Venn diagram that $E1$ and $E2$ do not overlap and hence are mutually exclusive. But entering the workforce instead of going to college has an opportunity cost as well. Although the answer may be clear, we list both the sets.

If two events are considered disjoint events, then the probability of both events occurring at the same time is zero. When you flip a coin, it’s either going to land with heads or tails facing up — There’s no chance that both sides will be facing up. If two events are mutually exclusive, only one of them can occur.

## Perimeter of Closed Figures: Definitions, Explanation, Examples

Add mutually exclusive to one of your lists below, or create a new one. 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. Mutually exclusive events are those events that can not take place at the same time. For instance, you can not run backwards and forwards at the same time. 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.

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

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. This information is educational, and is not an offer to sell or a solicitation of an offer to buy any security. This information is not a recommendation to buy, hold, or sell an investment or financial product, or take any action.

## Venn Diagram Representation of Mutually Exclusive Events

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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. The concept of mutually exclusive events offers numerous applications in finance.

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. Two events are said to be dependent if the occurrence of one event changes the probability of another event. Two events are said to be independent events if the probability of one event does not affect the probability of another event. If two events are mutually exclusive, they are not independent. Also, independent events cannot be mutually exclusive.

## Solved Examples on Mutually Exclusive Events

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. Mutually exclusive events are the events that cannot occur or happen at the same time.

Two mutually exclusive events are neither necessarily independent nor dependent. Further, if two events are considered disjoint events, then the probability of both events occurring at the same time will be zero. Let us learn more about this concept in this short lesson along with solved examples.

We know that it is not possible for mutually exclusive events to occur simultaneously. We cannot get both heads and tails while tossing a coin. So “getting a head” and “getting a tail” are mutually exclusive events. We know that mutually exclusive events cannot occur at the same time. In this case, the sum of their probability is exactly 1.