Event space \(\mathcal{F}\)

• The event space consists of all possible combinations of outcomes (Events \(E \subseteq \Omega\)).

• Note that an outcome is an element of \(\Omega\), an Event is a subset. Can consist of one or many outcomes.

• For a discrete sample space with \(n\) elements, there are \(2^n\) Events in \(\mathcal{F}\)

• Example: Consider an experiment with 3 outcomes \(\Omega = \{A, B , C\}\). Then:

\[ \mathcal{F} = \{\emptyset, \{A\}, \{B\},\{C\},\{A, B\},\{A, C\},\{B, C\}, \{A,B, C\}\} \]