Describe the sample space for the indicated experiment: $A$ die is thrown two times.

When a die is thrown,the possible outcomes are $1, 2, 3, 4, 5,$ or $6$.
When a die is thrown two times,the sample space $S$ is given by the set of all ordered pairs $(x, y)$ where $x$ and $y$ represent the outcomes of the first and second throw respectively,such that $x, y \in \{1, 2, 3, 4, 5, 6\}$.
The total number of elements in this sample space is $6 \times 6 = 36$.
The sample space $S$ is:
$S = \{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)\}$