When two dice are rolled, each die has 6 faces, resulting in $6 \times 6 = 36$ total possible outcomes.

Step 1: Outcomes for a sum of 12

To get a sum of 12, both dice must show a 6:

• (6, 6)

Thus, there is 1 outcome for a sum of 12.

Step 2: Outcomes for a sum of 10

To get a sum of 10, the following pairs of dice can occur:

• (4, 6)
• (5, 5)
• (6, 4)

Thus, there are 3 outcomes for a sum of 10.

Step 3: Total outcomes

There are 1 outcome for a sum of 12 and 3 outcomes for a sum of 10, so in total there are $1 + 3 = 4$ favorable outcomes.

Step 4: Probability

The total number of possible outcomes when rolling two dice is 36, and there are 4 favorable outcomes. Therefore, the probability of getting a sum of 12 or 10 is:

$\frac{4}{36} = \frac{1}{9}$

Final Answer:

The probability of getting a sum of 12 or 10 is $\frac{1}{9}$.

Would you like any additional details or have any questions?

Here are 5 related questions:

1. What is the probability of rolling a sum of 7 with two dice?
2. How many possible outcomes are there for rolling a sum of 11?
3. What is the probability of rolling two dice and getting a sum less than 5?
4. How does the probability change if we use three dice instead of two?
5. What is the probability of rolling the same number on both dice?

Tip: When calculating probabilities, always ensure the total number of possible outcomes is correctly accounted for before focusing on favorable outcomes.