What is the probability of rolling a sum of 7 with two six-sided dice?

To determine the probability of rolling a sum of 7 with two six-sided dice, we first need to consider the total number of possible outcomes. Each die has 6 faces, resulting in a total of 6 x 6 = 36 outcomes when rolling two dice.

Next, we identify the combinations of numbers on the two dice that result in a sum of 7. The possible combinations are as follows:

1. (1, 6)
2. (2, 5)
3. (3, 4)
4. (4, 3)
5. (5, 2)
6. (6, 1)

Counting these combinations, we find there are 6 ways to achieve a sum of 7.

To find the probability, we divide the number of favorable outcomes by the total number of outcomes. Thus, the probability of rolling a sum of 7 is the number of successful outcomes (6) divided by the total outcomes (36):

[ \text{Probability} = \frac{6}{36} = \frac{1}{6} ]

This calculation shows that the probability of rolling a sum of 7 with two six-sided dice is indeed 1/6, verifying