1. What is Two Dice Probability?

The probability of getting a specific sum when rolling two standard six-sided dice. There are 36 possible outcomes (6 × 6) with sums ranging from 2 to 12.

2. How Does the Calculator Work?

The calculator uses the probability formula:

Where:

• \( P \) — Probability (0-1)
• favorable outcomes — Number of dice combinations that produce the desired sum

Explanation: Each die has 6 faces, so there are 6 × 6 = 36 possible outcomes when rolling two dice.

3. Probability Distribution

Details: The probability distribution is symmetric with 7 being the most likely sum (6/36 = 16.67%) and 2 and 12 being the least likely (1/36 = 2.78% each).

4. Using the Calculator

Tips: Enter any integer sum between 2 and 12 to see the probability of rolling that sum with two standard dice.

5. Frequently Asked Questions (FAQ)

Q1: Why are some sums more likely than others?
A: There are more combinations that add up to middle numbers (like 7) than extreme numbers (like 2 or 12).

Q2: What's the probability of rolling doubles?
A: 6/36 = 1/6 ≈ 16.67% (there are 6 possible doubles: 1-1, 2-2, ..., 6-6).

Q3: What's the expected value when rolling two dice?
A: The expected value is 7, which is the average sum you'd get over many rolls.

Q4: How does this change with different dice?
A: For n-sided dice, there are n² possible outcomes. The probability distribution changes accordingly.

Q5: What's the probability of rolling at least a certain sum?
A: You would sum the probabilities of all sums equal to or greater than your target number.