Why are the outcomes (1, 2) and (2, 1) different when two dice are rolled?

In the study of probability theory, the outcomes (1, 2) and (2, 1) are considered distinct because the two dice are treated as identifiable—for instance, by a difference in color or by their position as individual objects.1

When rolling two dice, the sample space consists of 36 possible outcomes, each represented as an ordered pair (i, j), where i and j denote the specific face showing on each individual die. Because the dice are identifiable, the outcome where the first die shows 1 and the second shows 2 is a different event from the outcome where the first die shows 2 and the second shows 1. Recognizing these as separate outcomes is essential for correctly calculating probabilities, such as determining the likelihood of a specific sum occurring.1