Question

Find the sample space associated with the experiment of rolling a pair of dice (plural of die) once. Also find the number of elements of the sample space.

Answer 1

Let one die be blue and the other be green. Suppose ${}^{\prime }{1}^{\prime }$ appears on blue die and ${}^{\prime }{2}^{\prime }$ appears on green die. We denote this outcome by an ordered pair $(1,2)$. Similarly, if ${}^{\prime }{3}^{\prime }$ appears on blue die and ${}^{\prime }{5}^{\prime }$ appears on green die, we denote this outcome by $(3,5)$ and so on. Thus, each outcome can be denoted by an ordered pair $(x,y),$ where $x$ is the number appeared on the first die (blue die) and $y$ appeared on the second die (green die). Thus, the sample space is given by S={$(x,y)x$ is the number on blue die and $y$ is the number on grey die}
We now list all the possible outcomes (figure)
Number of elements (outcomes) of the above sample space is $6\times 6$ i.e., $36$