https://file.aiquickdraw.com/mathbot/file/1730215180873okmuukws.jpg

To solve this problem, we need to find the probability that the sum of the two dice is either 3 or 9.

### Step 1: Calculate the Total Possible Outcomes
Since each die has 6 faces, rolling two dice gives a total of:
\[
6 \times 6 = 36 \text{ possible outcomes}
\]
This matches the grid shown in the image, with 36 pairs listed.

### Step 2: Find Outcomes Where the Sum is 3
Possible pairs that sum to 3 are:
1. (1, 2)
2. (2, 1)

There are **2 outcomes** where the sum is 3.

### Step 3: Find Outcomes Where the Sum is 9
Possible pairs that sum to 9 are:
1. (3, 6)
2. (4, 5)
3. (5, 4)
4. (6, 3)

There are **4 outcomes** where the sum is 9.

### Step 4: Combine Outcomes
The outcomes with a sum of either 3 or 9 are:
\[
2 + 4 = 6 \text{ outcomes}
\]

### Step 5: Calculate the Probability
The probability of getting a sum of 3 or 9 is given by:
\[
\frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{6}{36} = \frac{1}{6}
\]

### Answer
The probability that the sum of the dice is 3 or 9 is:
\[
\frac{1}{6}
\]

Would you like more details on how these sums were identified or have other questions?

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Here are five related questions to expand your understanding:
1. What is the probability of rolling a sum of 7 with two dice?
2. How would the probability change if we wanted a sum of 4 or 8?
3. If we rolled three dice, what would the probability be for a sum of 9?
4. How many outcomes give a sum greater than 8 with two dice?
5. What is the probability of rolling doubles (like (1,1), (2,2), etc.)?

**Tip:** When calculating probabilities with dice, listing all possible outcomes helps ensure no combinations are missed.

Determine the probability that the sum of the dice is 3 or 9.

Learn how to calculate the probability of rolling a sum of 3 or 9 with two dice. This problem covers basic probability concepts, sample space analysis, and probability calculation. Suitable for students in Grades 6-8.

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