$ S = \{\text{set of all outcomes}\} $ A **Sample Space** (denoted $S$ or $\Omega$) is the set of all possible outcomes of a random experiment. --- > [!question]- Sample Space of Rolling Two Dice {💡 Example} > What is the **sample space** of an experiment in which two six-sided are rolled? 🎲🎲 > > > [!answer]- Answer > > Each die can show 1 through 6, so the sample space is > > $ S = \{(i, j) : i, j \in \{1,2,3,4,5,6\}\} $ > > This set contains $6 \times 6 = 36$ equally likely outcomes.