Experiment/Examples/Throwing a 6-Sided Die

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:
 * $\forall \omega \in \Omega: \map \Pr \omega = \dfrac 1 6$