How can the event that two dice add to six be represented within a sample space?

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sample space for a pair of dice — probability theory Sample space for a pair of dice.

In probability theory, the sample space for tossing two dice consists of 36 possible outcomes, represented as ordered pairs $(i, j)$ , where $i$ and $j$ are the values showing on each die (1 through 6).

An event is defined as a subset of the sample space. The event that the sum of the two dice equals six is represented by the following subset of five outcomes:

{(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)}

Because each of the 36 outcomes in the sample space is considered equally likely, the probability of this event is the ratio of the number of favorable outcomes to the total number of outcomes, which is $5 / 36$ .1