# Impossible event

The impossible event is one that can never happen.

In probability theory, the impossible event is one that never occurs. It is usually designated with the empty set. It is a fundamental concept in the introduction to probability theory. It is the opposite of the safe event.

It is actually a theoretical concept to give mathematical form to probabilistic problems. Impossible events are all those events that are outside the sample space. That is, from the set of possible outcomes.

## Sample space, impossible event and safe event

There is a close relationship between these three concepts. Hence, we dedicate a section to differentiate and relate these three terms:

• Impossible event: It is one that never happens. It is denoted by the symbol of the empty set. It is the opposite of a certain event.
• Safe event: It is that event that always occurs, without exception. It is made up of the elements of the sample space. In other words, for all elementary events. It is the opposite of the impossible event.
• Sample space: It is composed of all elementary events. Thus, the safe event coincides with the elements that make up the sample space.

## Example of an impossible event

To illustrate the concept of an impossible event more clearly, we are going to give an example with a die. The die has 6 sides and is perfect. Each face, as usual, has a number. So, the impossible event will be the one that never occurs. Here are several examples of impossible events:

• That a number greater than 8 comes out: It is an impossible event. If the die has 6 faces with numbers from 1 to 6, it can never be greater than 8.
• Output a number less than zero: A result less than zero is an impossible event. We know that a number between 1 and 6 will always come up. Therefore, we will not have results below 1.
• That a number greater than or equal to 6 comes out: It is not an impossible event. It can come out on 6, since we have added the same condition as 6. Therefore, we cannot guarantee that it will never occur.

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