What is the probability that the sum of two dice rolled is between 2 and 12, inclusive?

To determine the probability that the sum of two dice rolled is between 2 and 12, inclusive, we first need to ascertain the possible outcomes when rolling two dice. The minimum sum achieved by rolling two dice is 2 (which occurs only when both dice show 1). The maximum sum is 12 (which occurs only when both dice show 6).

When evaluating the sums that can be derived from two dice, all possible sums range from 2 to 12. This means every possible outcome that results from rolling two dice will produce a sum within this range. The total number of combinations when rolling two dice is 36, as each die has 6 faces (6 x 6 = 36).

Since all outcomes (sums from 2 to 12) are included in the range we are examining, this implies that every possible outcome falls within the specified range. Therefore, the probability of rolling a sum between 2 and 12 is the ratio of favorable outcomes (sums from 2 to 12) to the total outcomes (which is always 36). In this case, the number of favorable outcomes is equal to the total number of outcomes, leading to a probability of 1.

This illustrates that the