To find the likelihood that a student who has a sibling does not have a pet, we need to use the concept of conditional probability. Specifically, we are interested in [tex]\( P(\text{No pets} \mid \text{Siblings}) \)[/tex], which represents the probability of a student not having a pet given that they have a sibling.
Using the data from the table, the steps are as follows:
1. Identify the total probability of having a sibling: From the table, we can see that the total probability of a student having a sibling is 0.75.
2. Identify the joint probability of having no pets and having a sibling: The table shows that the relative frequency of students who have no pets and have siblings is 0.45.
3. Use the formula for conditional probability:
[tex]\[
P(\text{No pets} \mid \text{Siblings}) = \frac{P(\text{No pets and Siblings})}{P(\text{Siblings})}
\][/tex]
Substituting in the values:
[tex]\[
P(\text{No pets} \mid \text{Siblings}) = \frac{0.45}{0.75}
\][/tex]
4. Calculate the values:
[tex]\[
P(\text{No pets} \mid \text{Siblings}) = 0.6
\][/tex]
5. Express the probability as a percentage:
[tex]\[
P(\text{No pets} \mid \text{Siblings}) \times 100 = 60\%
\][/tex]
Therefore, the correct answer is:
C. [tex]\(60\%\)[/tex]
