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: $\Sigma = \set {\forall \omega \in \Omega: \omega \ge 4}$.

$(3): \quad$ The result is a prime number:

The event space of $\EE$ is: $\Sigma = \set {2, 3, 5}$.

The probability measure is defined as:

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

Sources

• 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $1$: Events and probabilities: $1.1$: Experiments with chance