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Probability calculation is the process used to determine how likely an event is to occur. When rolling two 12-sided dice, each die has 12 faces, numbered 1 through 12. Each face is equally likely to land face up. This means each face has a probability of \(\frac{1}{12}\).

When calculating the total number of possible outcomes for two dice, you multiply the number of faces on the first die by the number of faces on the second die:
\[ \text{Number of Pairs} = 12 \times 12 = 144 \] This means there are 144 unique combinations of rolls.

To find the probability of a specific sum, like 13, we count how many ways we can get that sum. For instance, to get 13:
- Roll (1, 12)
- Roll (2, 11)
- Roll (3, 10)
- And so on, up to (12, 1)
There are 12 ways to get this sum. 

So, the probability of rolling a sum of 13 is:
\[ \text{Probability} = \frac{12}{144} = \frac{1}{12} = 0.0833 \] Therefore, the probability is about 8.33%.

The sum of dice rolls is simply the total value when adding the faces of both dice. For two 12-sided dice, the smallest sum occurs when both dice land on 1 and is \(\text{1+1=2}\).
The greatest possible sum is when both dice land on 12, so we get:
\[ \text{Greatest sum} = 12 + 12 = 24 \]

When considering which sum is most likely, we look at the distribution of all possible sums. This distribution forms a symmetrical pattern. The midpoint between the smallest and greatest sum gives us the most likely sum:
\[ \text{Most likely sum} = \frac{2 + 24}{2} = 13 \] This is because the pairs of numbers around this midpoint have the highest number of combinations.

Thus, the sum of 13 is the most probable result when rolling two 12-sided dice.

Dice combinations refer to the unique pairs you can get when rolling two dice. For example, a roll of (3, 4) is different from (4, 3), making each pair unique.
When rolling two dice, each die has 12 outcomes. Together, these create a total of:
\[ \text{Number of pairs} = 12 \times 12 = 144 \] combinations.

To understand this concept better, think about listing all numbers from 1 to 12 on the first die and repeating this for the second die. Pairing each number from the first die with each from the second results in 144 different pairs.

When focusing on a specific sum, like 13, remember that different pairs result in the same sum. For instance:
(1, 12), (2, 11), (3, 10) ... up to (12, 1).
Each of these pairs totals to 13, and we've identified 12 such pairs.

So, the dice combinations help us understand how many ways a specific outcome can be reached, which is essential for calculating probabilities.