I assume that the two numbers are on the faces of the dice.

Let and ; then is the domain of . The definition says that is an -valued random variable if for all . That is, for any subset of values that may have, the set of outcomes from that produce an answer in is a legitimate event, i.e., belongs to the set of events . For this example, this fact is obvious because includes all possible subsets of .

In contrast, is not a random variable with respect to and . E.g., consider .