When you roll two dice, there are 36 possible outcomes because each die has 6 sides, and there are 6 * 6 = 36 total combinations.
To find the probability of each possible outcome, you can create a table showing all the possible combinations and their probabilities. Here are the outcomes and their probabilities:
1. Rolling a sum of 2: There's only one way to get a sum of 2 (1 on the first die and 1 on the second die). So, the probability is 1/36.
2. Rolling a sum of 3: There are two ways to get a sum of 3 (1+2 and 2+1). So, the probability is 2/36, which simplifies to 1/18.
3. Rolling a sum of 4: There are three ways to get a sum of 4 (1+3, 2+2, and 3+1). So, the probability is 3/36, which simplifies to 1/12.
4. Rolling a sum of 5: There are four ways to get a sum of 5 (1+4, 2+3, 3+2, and 4+1). So, the probability is 4/36, which simplifies to 1/9.
5. Rolling a sum of 6: There are five ways to get a sum of 6 (1+5, 2+4, 3+3, 4+2, and 5+1). So, the probability is 5/36.
6. Rolling a sum of 7: There are six ways to get a sum of 7 (1+6, 2+5, 3+4, 4+3, 5+2, and 6+1). So, the probability is 6/36, which simplifies to 1/6.
7. Rolling a sum of 8: There are five ways to get a sum of 8 (2+6, 3+5, 4+4, 5+3, and 6+2). So, the probability is 5/36.
8. Rolling a sum of 9: There are four ways to get a sum of 9 (3+6, 4+5, 5+4, and 6+3). So, the probability is 4/36, which simplifies to 1/9.
9. Rolling a sum of 10: There are three ways to get a sum of 10 (4+6, 5+5, and 6+4). So, the probability is 3/36, which simplifies to 1/12.
10. Rolling a sum of 11: There are two ways to get a sum of 11 (5+6 and 6+5). So, the probability is 2/36, which simplifies to 1/18.
11. Rolling a sum of 12: There's only one way to get a sum of 12 (6+6). So, the probability is 1/36.
These are the probabilities of each possible outcome when rolling two dice.