Experiment/Examples/Throwing a 6-Sided Die

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Example of Experiment

Let $\EE$ be the experiment of throwing a standard $6$-sided die.

The sample space of $\EE$ is $\Omega = \set {1, 2, 3, 4, 5, 6}$.
Various events can be identified:
$(1): \quad$ The result is $3$:
The event space of $\EE$ is: $\Sigma = \set 3$.
$(2): \quad$ The result is at least $4$:
The event space of $\EE$ is: $\Sigma = \set {\forall \omega \in \Omega: \omega > 4}$.
$(3): \quad$ The result is a prime number:
The event space of $\EE$ is: $\Sigma = \set {2, 3, 5}$.
The probability measure is defined as:
$\forall \omega \in \Omega: \map \Pr \omega = \dfrac 1 6$