$A \subseteq S, \quad P(A) = \sum_{\omega \in A} P(\{\omega\})$ An Event ($A$) is any subset of the sample space $S$ to which a probability can be assigned; it represents a collection of outcomes that share some property of interest. Simple events contain a single outcome; compound events contain two or more. Set operations on events have direct probabilistic interpretations: $A \cup B$ is "$A$ or $Bquot;, $A \cap B$ is "$A$ and $Bquot;, and $A^c$ is "not $Aquot;. An event occurs if the realized outcome $\omega$ belongs to that subset. > [!example]- Defining Events for a Die Roll {💡 Example} > A fair six-sided die is rolled. Let $A$ = "the result is even" and $B$ = "the result is greater than 4". List the outcomes in $A$, $B$, $A \cap B$, and $A \cup B$. > > > [!answer]- Answer > > $A = \{2, 4, 6\}, \quad B = \{5, 6\}$ > > $A \cap B = \{6\}, \quad A \cup B = \{2, 4, 5, 6\}$ > > $P(A \cap B) = \frac{1}{6}, \quad P(A \cup B) = \frac{4}{6} = \frac{2}{3}$