Find the sample space associated with the experiment of rolling a pair of dice (one is blue and the other red) once. Also,find the number of elements of this sample space.

Suppose $1$ appears on the blue die and $2$ on the red die. We denote this outcome by an ordered pair $(1, 2)$. Similarly,if $3$ appears on the blue die and $5$ on the red die,the outcome is denoted by the ordered pair $(3, 5)$.
In general,each outcome can be denoted by the ordered pair $(x, y)$,where $x$ is the number appearing on the blue die and $y$ is the number appearing on the red die.
Therefore,the sample space $S$ is given by:
$S = \{(x, y) : x \in \{1, 2, 3, 4, 5, 6\}, y \in \{1, 2, 3, 4, 5, 6\}\}$
The number of elements in this sample space is $6 \times 6 = 36$.
The sample space is:
$S = \{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)\}$