Why is the probability of rolling a sum of six with two fair dice equal to 5/36?

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

In probability theory, the probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes in the sample space.

When tossing two fair dice, each die has six faces, resulting in a total of $6 \times 6 = 36$ equally likely outcomes. These outcomes are represented as ordered pairs $(i, j)$ , where $i$ and $j$ are the values shown on each die.1

To find the probability of the sum equaling six, we identify all favorable outcomes within the sample space:
* (1, 5)
* (2, 4)
* (3, 3)
* (4, 2)
* (5, 1)

There are exactly 5 such outcomes. By dividing the number of favorable outcomes (5) by the total number of possible outcomes (36), we arrive at the probability of 5/36.1