Experiment/Examples/Tossing 2 Coins

Example of Experiment
Let $\mathcal E$ be the experiment of tossing $2$ coins.

The sample space of $\mathcal E$ is:
 * $\Omega = \set {\tuple {\mathrm H, \mathrm H}, \tuple {\mathrm H, \mathrm T}, \tuple {\mathrm T, \mathrm H}, \tuple {\mathrm T, \mathrm T} }$

where $\mathrm H$ denotes heads and $\mathrm T$ denotes tails.

Suppose we are interested only in whether the coins fall alike ($\mathrm A$) or different ($\mathrm D$).

Then the sample space of $\mathcal E$ is: $\Sigma = \set {\forall \omega \in \Omega: \omega > 4}$.
 * $\Omega = \set {\mathrm A, \mathrm D}$