# 5 Examples of Mutually Exclusive Events

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We say that two events are mutually exclusive if the occurrence of one event guarantees the non-occurrence of the other event. The two mutually exclusive events cannot occur simultaneously. In this article, we list out seven basic examples of mutually exclusive events.

### Examples of Mutually Exclusive Events:

1. Suppose that two coins are thrown. Let A be the event that we get two heads and B be the event that we get two tails. Clearly A and B cannot occur simultaneously and hence are mutually exclusive events. Notice that it is possible neither A nor B occurs. For instance, we may get heads on the first toss and tails on the second toss.
2. Suppose that a die is thrown. Let A be the event that we get a number less than or equal to 2 and B be the event that we get a number greater than 4. The two events cannot occur simultaneously although it is possible that neither of the two events occur. For example if we obtain the number 3 then neither of the events A or B occurs.
3. Failing or passing in a particular course at the university. Notice that the two outcomes are not only mutually exclusive but are also exhaustive meaning that one of them MUST occur. The students must either receive a passing grade or fail in the course.
4. When waiting for a train at the train station let A be the event that a person waits less than 5 minutes and let B be the event that the person waits for more than 10 minutes. The events A and B are mutually exclusive.
5. Suppose a student is randomly chosen from a class. Then his height can either be taller than 5 feet or shorter than 5 feet.

### Examples of events that are NOT Mutually Exclusive:

1. If a die is thrown, let A be the event that we get an even number and B be the event that we get a number less than 4. We have that A = {2, 4, 6} and B = {1, 2, 3}. The events are NOT mutually exclusive because we if we get 2 on the uppermost face on the die then the events A and B occur simultaneously.
2. Suppose a student is randomly chosen from a class. Let A be the event that the height of the student is greater than 5 feet and let B be the event that the student weighs more than 140 pounds. Clearly, the events are NOT mutually exclusive since it is possible that a student is taller than 5 feet and weighs more than 140 pounds.

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