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. **Calculate the sample space:** For the first die, possible outcomes are $\{1,2,3,4,5,6\}$. For the second die, possible outcomes are also $\{1,2,3,4,5,6\}$. 5. **Combine outcomes:** The sample space $S$ is all ordered pairs $(a,b)$ where $a$ is the result of the first die and $b$ is the result of the second die. 6. **Size of sample space:** Total outcomes = $6 \times 6 = 36$. 7. **Final sample space:** $$ S = \{(1,1), (1,2), \ldots, (1,6), (2,1), (2,2), \ldots, (6,6)\} $$ This means every combination of numbers from 1 to 6 on both dice is possible.