Count equally likely outcomes

A fair six-sided die has six equally likely outcomes. For an even result, the favorable outcomes are 2, 4 and 6.

That gives 3 favorable outcomes out of 6: 3/6 = 1/2. Counting works because each outcome in the list has the same probability.

Roll two fair dice independently. Each of the first die’s six results can pair with all six results of the second, making 6 × 6 = 36 equally likely ordered outcomes.

For a sum of 7, the pairs are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1). There are six, so the probability is 6/36 = 1/6. A sum is not one equally likely outcome.

Roll the same two fair dice independently. This time, find the probability that their sum is 8.

Use the grid to count every matching ordered pair. There are still 36 equally likely outcomes, but the favorable count can change.