Let's solve the problem step-by-step.
1. Understanding the Problem:
We need to find the probability that the sum of the numbers rolled on two dice is [tex]\(7\)[/tex].
2. Total Possible Outcomes:
Each die has 6 faces, labeled from 1 to 6. When rolling two dice, the total number of possible outcomes is the product of the number of faces on each die:
[tex]\[
\text{Total possible outcomes} = 6 \times 6 = 36
\][/tex]
3. Favorable Outcomes:
We need to determine how many outcomes result in the sum being [tex]\(7\)[/tex]. These outcomes are:
[tex]\[
(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
\][/tex]
There are 6 such outcomes.
4. Calculate the Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
Substituting the values, we get:
[tex]\[
\text{Probability} = \frac{6}{36} = \frac{1}{6}
\][/tex]
Therefore, the probability that the sum of the numbers rolled is [tex]\(7\)[/tex] is [tex]\( \frac{1}{6} \)[/tex].
So, the answer is:
[tex]\[
\boxed{\frac{1}{6}}
\][/tex]
Hence, the correct option is C) [tex]\( \frac{1}{6} \)[/tex].
