we roll a 6-sided die twice, what is the probability of getting 2,5

When rolling a 6-sided die twice, the possible outcomes for the sum of the rolls range from 2 to 12. Let's calculate the probability of getting a sum of 2 or 5.

### 1. Probability of getting a sum of 2:
- The only way to get a sum of 2 is by rolling a 1 on both dice: \( (1,1) \).
- There is 1 favorable outcome.

### 2. Probability of getting a sum of 5:
- To get a sum of 5, the following outcomes are possible: \( (1,4), (2,3), (3,2), (4,1) \).
- There are 4 favorable outcomes.

### Total Possible Outcomes:
- Since each die has 6 faces, and they are rolled independently, the total number of possible outcomes is \( 6 \times 6 = 36 \).

### Calculating Probabilities:
- **Probability of getting a sum of 2**: \( \frac{1}{36} \).
- **Probability of getting a sum of 5**: \( \frac{4}{36} = \frac{1}{9} \).

### Combined Probability:
To find the probability of getting either a sum of 2 **or** a sum of 5, we add these probabilities:

\[
\text{Combined Probability} = \frac{1}{36} + \frac{4}{36} = \frac{5}{36}
\]

So, the probability of getting a sum of either 2 or 5 is \( \frac{5}{36} \).

Would you like more details or have any questions?

Here are five related questions:
1. What is the probability of getting a sum of 7 or 11 when rolling two 6-sided dice?
2. How do you calculate the probability of getting a specific sum with two dice?
3. What is the probability of getting a sum of 8 with two 6-sided dice?
4. How does the probability distribution of sums change with more dice?
5. What are the most likely sums when rolling two 6-sided dice, and why?

**Tip:** When calculating probabilities for dice rolls, consider all possible combinations of dice that result in the desired outcome.

Explore the probability of rolling a sum of 2 or 5 with two 6-sided dice. Learn how to calculate probabilities for specific outcomes when rolling multiple dice. Suitable for Grades 7-9.

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