To find the probability of rolling a sum of 7 with two dice, we can use the method of counting favorable outcomes and dividing by the total number of possible outcomes.
For two dice, each die has 6 sides, numbered 1 to 6. The number of possible outcomes when rolling two dice is the product of the number of sides on each die, which is 6 × 6 = 36.
Now let’s count the favorable outcomes. We are looking for pairs of rolls that add up to 7. There are six such pairs:
1. ((1,6))
2. ((2,5))
3. ((3,4))
4. ((4,3))
5. ((5,2))
6. ((6,1))So there are 6 favorable outcomes. Therefore, the probability of rolling a sum of 7 with two dice is the ratio of favorable outcomes to the total number of outcomes:
$$P(\text{sum}=7) = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{6}{36} = \frac{1}{6}.$$
Thus, the probability of rolling a sum of 7 with two dice is $\frac{1}{6}$, or approximately 16.67%.