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.