1. **State the problem:** We need to find the sample space when two dice are tossed simultaneously. 2. **Understanding the problem:** Each die has 6 faces numbered from 1 to 6. 3. **Formula and rules:** The sample space for two independent events is the Cartesian product of the individual sample spaces. 4. **Sample space for one die:** $S_1 = \{1, 2, 3, 4, 5, 6\}$ 5. **Sample space for two dice:** $S = S_1 \times S_1 = \{(a,b) \mid a \in S_1, b \in S_1\}$ 6. **Enumerate the sample space:** The sample space consists of all ordered pairs $(a,b)$ where $a$ and $b$ are numbers from 1 to 6. 7. **Total number of outcomes:** Since each die has 6 outcomes, total outcomes are $6 \times 6 = 36$. 8. **Final answer:** The sample space is $$ \{(1,1), (1,2), \ldots, (1,6), (2,1), (2,2), \ldots, (6,6)\} $$ with 36 equally likely outcomes.