# Elemental event

An elementary event is each of the possible outcomes of a random experiment.

When we speak of an elementary event, we speak of a simple result. It is the simplest result that we can obtain from a random experiment. Thus, for example, rolling a die once is made up of six elementary events. Each of the six possible outcomes of rolling the die once is an elemental event or elemental outcome.

In probability theory it is the first concept that is studied. And, it is worth mentioning, that it is studied together with the concept of sample space. In such a way, that the sample space is composed of all the elementary events.

Another very simple example would be to toss a coin only once. The elementary events of the toss of a coin are two: heads and tails.

## Elementary event example

Although we have already provided two examples that make the meaning of an elementary event clear, it should be noted that it is not always so simple. Sometimes the random experiment you want to study is not so simple. Suppose, then, a somewhat more complex example.

Let's imagine that we have an urn. Inside this urn are 5 red balls, 4 blue balls and 2 white balls. The random experiment consists of taking a ball and seeing which ball we have taken. The elementary events of this experiment will be:

Ω = (Br1, Br2, Br3, Br4, Br5, Ba1, Ba2, Ba3, Ba4, Bb1, Bb2)

That is, an elementary event would be to remove, for example, the red ball 1 (br1). Another elementary event could be to remove cue ball 2 (bb2). In this way, the extraction of each one of the balls is an elementary event.

## Difference between event and elemental event

The concepts of event and elementary event are closely related. But no, they are not the same. An event is usually somewhat larger and may or may not coincide with the elemental event. For example, on the roll of a die:

• Elemental event: An example of an elemental event on the roll of a die would be 3.
• Event: An example of an event could be that a number greater than 3. For this event to be fulfilled, it is enough that the number 4, 5 or 6 appears as a result of the launch.

To differentiate them, instead of just "event" it can be named as a compound event.

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