How is a sample space constructed for rolling two distinguishable dice?

In probability theory, a sample space is defined as the set of all possible outcomes of an experiment.12

To construct the sample space for rolling two distinguishable dice, each outcome is represented as an ordered pair $(i,j)$, where $i$ and $j$ denote the values showing on the first and second die, respectively. Because the dice are distinguishable—for instance, by a difference in color—the outcome $(1,2)$ is distinct from $(2,1)$.2

Since each die has six faces, there are $6\times 6=36$ possible outcomes in the sample space. In this model, these 36 outcomes are typically assumed to be equally likely. Consequently, the probability of any specific event is calculated as the ratio of the number of outcomes favorable to that event to the total number of outcomes in the sample space.2