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 blue die and $2$ on the red dic. We denote this outcome by an ordered pair $( 1,2 )$. Similarly, if $'3'$ appears on blue die and  $'5'$ on red, 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 appeared on the blue die and $y$ is the number appeared on the red die. Therefore, this sample space is given by

$S=\{(x, y): x$ is the number on the blue die and $y$ is the number on the red die $\}$ The number of elements of this sample space is $6 \times 6=36$ and the sample space is given below :

$\{(1,1),\,(1,2),\,(1,3),\,(1,4)$,  $(1,5),\,(1,6)\,,(2,1)$, $(2,2),\,(2,3),\,(2,4),\,(2,5),\,(2,6)$

$(3,1),\,(3,2)\,,(3,3)\,,(3,4)$,  $(3,5),\,(3,6)\,,(4,1)$,  $(4,2),\,(4,3),\,(4,4),\,(4,5),\,(4,6)$

$(5,1)\,,(5,2),\,(5,3),\,(5,4)$,  $(5,5),\,(5,6),\,(6,1),\,(6,2)$,  $(6,3)\,,(6,4),\,(6,5),\,(6,6)\}$