Event

An event is a summary of possible outcomes.
Therefore an event $E$ is always a subset of the sample space $\Omega$:

$E\subseteq\Omega$
!

Remember

An event occurs when the outcome of a trial is an element of the event.

Example

A die is rolled. One is interested in whether the outcome is an even or odd number. There are therefore two events:

$E_1=\{1, 3, 5\}$
$E_2=\{2, 4, 6\}$

If, for example, a 3 is now rolled, then event $E_1$ has occurred because $3 \in \{1, 3, 5\}$


Elementary event

Events that contain only one element are also called elementary events.

For example: $E=\{1\}$


Impossible event

If none of the possible outcomes of an experiment meets the condition described by an event, then the event is called an impossible event.
The event contains no element:

$E=\{\}$
i

Hint

The probability of an impossible event is 0.

Example

$E=\text{„7 is rolled“}=\{\}$
The event will never happen.


Sure event

If all possible outcomes of an experiment meet the condition described by an event, then the event is called a sure event.
The event contains all possible results:

$E=\Omega$
i

Hint

The probability of a sure event is 1.

Example

$E=\text{„Number less than 7“}$ $=\{1,2,3,4,5,6\}$
The event will always happen.