## Definition A ==Sample Space== (denoted $S$ or $\Omega$) is the set of all possible outcomes of a random experiment. Every probabilistic model begins by specifying the sample space, and every event is a subset of it. > [!example]- What is the sample space for rolling two distinguishable six-sided dice? > 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.