Odds of rolling numbers sum total of 2-6 with two six sided dice

Let's analyze the probability of obtaining a sum between 2 and 6 when rolling two six-sided dice. Here’s a breakdown:

1. **Possible sums for two dice:** When rolling two six-sided dice, the possible sums range from 2 (1+1) to 12 (6+6).
2. **Desired sums (2 to 6):** We need to calculate the number of ways to achieve sums of 2, 3, 4, 5, and 6.

### Step-by-Step Calculation

1. **Sum of 2:** Only 1 way: (1,1).
2. **Sum of 3:** 2 ways: (1,2) and (2,1).
3. **Sum of 4:** 3 ways: (1,3), (2,2), and (3,1).
4. **Sum of 5:** 4 ways: (1,4), (2,3), (3,2), and (4,1).
5. **Sum of 6:** 5 ways: (1,5), (2,4), (3,3), (4,2), and (5,1).

### Total Possible Outcomes
Since each die has 6 sides, there are \(6 \times 6 = 36\) possible outcomes when rolling two dice.

### Probability Calculation
Adding up the favorable outcomes:
\[
1 + 2 + 3 + 4 + 5 = 15
\]
Thus, the probability of rolling a sum between 2 and 6 is:
\[
\frac{15}{36} = \frac{5}{12} \approx 0.4167
\]

### Answer
The probability of rolling a sum between 2 and 6 with two six-sided dice is \( \frac{5}{12} \) or approximately 41.67%.

Would you like further explanation on any part?

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1. What is the probability of rolling a sum between 7 and 12?
2. How does the probability of rolling an even sum compare to an odd sum?
3. What is the probability of rolling a specific sum, such as exactly 7?
4. How do these probabilities change if using a 10-sided die?
5. What are the chances of rolling doubles on two six-sided dice?

**Tip:** In probability problems with dice, listing all possible combinations helps ensure accurate counting of outcomes.

Calculate the probability of rolling a sum between 2 and 6 with two six-sided dice. This problem includes combinatorial counting and basic probability calculations, with a step-by-step breakdown. Perfect for students in Grades 6-8.

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