A blue dye and a green dye are rolled. Find the probability that the sum is 12.

To find the probability that the sum of two rolled dice equals 12, we will assume that each dye has 6 sides (a standard die). Here's the step-by-step solution:

### 1. Possible Outcomes
- When rolling two dice, each die has 6 faces, giving a total of \( 6 \times 6 = 36 \) possible outcomes.

### 2. Favorable Outcomes
- The only way to get a sum of 12 is when both dice show a 6. So, there is only **1 favorable outcome**: (6, 6).

### 3. Probability Calculation
The probability is the ratio of favorable outcomes to the total possible outcomes:
\[
P(\text{sum} = 12) = \frac{1}{36}
\]

Thus, the probability that the sum of the two dice is 12 is \( \frac{1}{36} \).

Would you like more details on dice probability? Or do you have any other questions?

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Here are 5 related questions to further explore this topic:
1. What is the probability of rolling a sum of 7 with two dice?
2. How many outcomes result in a sum greater than 10?
3. What is the probability of rolling a sum of 2 with two dice?
4. How would the probability change if each die had 8 sides instead of 6?
5. How do you calculate the expected sum when rolling two dice?

**Tip:** Always count the total possible outcomes carefully, especially when dice or coins differ in number of sides.

Find the probability of rolling a sum of 12 with two six-sided dice. Learn how to calculate the total possible outcomes and identify the favorable outcomes. This problem covers basic probability concepts and is suitable for students in Grades 5-7.

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