# Elementary event

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

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

In probability theory it is the first concept that is studied. And, it should be mentioned, it is studied together with the concept of sample space. In such a way that the sample space is made up of all elementary events.

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

## Elementary event example

Although we have already provided two examples that make clear the meaning of elementary event, 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 we have an urn. Inside this urn there are 5 red balls, 4 blue balls and 2 white balls. The random experiment consists of taking a ball and seeing what ball we have taken out. 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 might be to take cue ball 2 (bb2). Thus, the extraction of each of the balls is an elementary event.

## Difference between event and elemental event

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

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

To differentiate them, instead of simply “event” it can be named as a composite event.