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The problem asks for the probability that the sum of the numbers on the top faces of two rolled dice will be greater than 10. Both dice are six-sided, with each side numbered from 1 to 6.

### Step-by-Step Solution:

1. **Total possible outcomes:**
   Since each die has 6 sides, the total number of possible outcomes when rolling two dice is:
   \[
   6 \times 6 = 36
   \]

2. **Outcomes where the sum is greater than 10:**
   We need to determine the pairs of numbers (one from each die) whose sum is greater than 10:
   - If the first die shows a 6, then the second die must show either a 5 or 6 to get a sum greater than 10:
     \[
     (6, 5), (6, 6)
     \]
     These are 2 outcomes.
   - If the first die shows a 5, then the second die must show a 6:
     \[
     (5, 6)
     \]
     This is 1 outcome.

   So, there are a total of \( 2 + 1 = 3 \) favorable outcomes.

3. **Probability:**
   The probability is the ratio of favorable outcomes to total outcomes:
   \[
   \frac{3}{36} = \frac{1}{12}
   \]

Therefore, the probability that the sum is greater than 10 is \( \frac{1}{12} \), which matches option **B**.

Would you like more details or have any questions?

### Related Questions:
1. What is the probability that the sum of the numbers on the top faces is exactly 10?
2. What is the probability that the sum of the numbers on the top faces is less than 5?
3. How many total possible outcomes result in an even sum?
4. What is the probability that both dice will land on the same number?
5. What is the probability of getting a sum of 7?

**Tip:** When calculating probabilities with dice, always remember to first compute the total possible outcomes to determine your sample space.

Two six-sided number cubes, each numbered 1 through 6, are rolled together. What is the probability that they will land with the numbers on the top face having a sum greater than 10?

This page explains how to calculate the probability of rolling a sum greater than 10 with two six-sided dice. It includes a step-by-step breakdown of the total and favorable outcomes, using key probability formulas. Suitable for middle school students, Grades 6-8.

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