Mutually Exclusive Events: Definition, Formulas, Solved Examples

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.

1. Two events are mutually exclusive if they cannot both occur at the same time.
2. Mutually exclusive events are events that can not occur simultaneously, i.e.
3. Stated differently, the occurrence of one event precludes the possibility of the other.
4. 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.
5. Understanding mutually exclusive events is essential in probability theory, and it can help us identify the probability of an event occurring.
6. Therefore, “India winning” and “Pakistan winning” are mutually exclusive events, as the occurrence of one excludes the other.

The green marbles are marked define mutually exclusive events with the numbers 1, 2, 3, and 4. If the events are not independent, then you cannot use the Addition Rule for Mutually Exclusive Events. This is because regardless of which project Company X chooses, it will still be able to afford to pursue Project C as well.

Mutually Exclusive: What It Means, With Examples

These are independent because the outcome of the first toss doesn’t affect the second. These are typically considered mutually exclusive (although light rain on a sunny day is possible in some cases). These are mutually exclusive because a number can’t be both even and odd. 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. Now let’s see what happens when events are not Mutually Exclusive.

These are mutually exclusive because a single card can’t be both a heart and a spade. Does one definition dominate the other in mathematics, and if so, which one? The red marbles are marked with the numbers 1, 2, 3, 4, 5, and 6.

In other words, if you want to calculate the probability of event A or event B happening, you simply add the probability of event A to the probability of event B. In each of these cases, the events are mutually exclusive because they cannot happen at the same time. Calculating probabilities for mutually exclusive events is an important concept in probability theory. The addition rule, Venn diagrams, and complements are all useful tools for approaching these problems. By understanding these methods and practicing with examples, we can become more proficient in calculating probabilities and making informed decisions in real-world scenarios. Mutually exclusive events are those that cannot happen at the same time.

1. The addition rule, Venn diagrams, and complements are all useful tools for approaching these problems.
2. This example demonstrates how combinations can be used to calculate probabilities in mutually exclusive events.
3. As the specialized piece of equipment cannot be used by both projects at the same time.
4. When a customer withdraws \(\$ 40\) from the machine, it dispenseseither two \(\$ 20\) bills or four \(\$ 10\) bills.
5. Before, going through this topic will discuss some important term or relations related to it.

Mutually Exclusive Events: Definition, Formulas, Solved Examples

Independent events are events where the occurrence of one event does not affect the probability of the other event occurring. In other words, the outcome of one event has no influence on the outcome of the other event. 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.

Since 11 is in both of these, the events are not mutually exclusive. 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.

Comparing definitions of mutually exclusive: disjoint events or zero probability of intersection?

However, this rule only applies to events that are mutually exclusive. If the events are not mutually exclusive, the addition rule cannot be used. The Addition Rule for Mutually Exclusive Events is an essential concept to understand when it comes to calculating probabilities. It is a straightforward way to calculate the probability of either of two mutually exclusive events happening.

If the events are not mutually exclusive, then the addition rule cannot be used. In the world of probability, an event space is a collection of all possible outcomes of a random experiment. It is the set of all possible results that can be obtained from the experiment.

Mutually Exclusive Events vs Independent Events

Mutually exclusive is 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. 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.

Probability Based on Coin

For instance, let’s consider an experiment where we roll two fair six-sided dice and want to find the probability of rolling either a sum of 7 or a sum of 11. A mutually exclusive event can make calculating probability a relatively simple task. Whereas non-mutually exclusive events can make figuring out probabilities a more complex task. Non-mutually exclusive events are events that can absolutely happen at the same time. Mutually exclusive events are two or more events that cannot occur simultaneously.