To solve this problem, we need to find the conditional probability. Specifically, we need to determine the probability that a student has a pet given that the student has a sibling.
We can use the formula for conditional probability:
[tex]\[ P(\text{Pet} \mid \text{Sibling}) = \frac{P(\text{Pet and Sibling})}{P(\text{Sibling})} \][/tex]
From the given data:
- [tex]\( P(\text{Pet and Sibling}) \)[/tex] is the proportion of students who have both pets and siblings, which is 0.3.
- [tex]\( P(\text{Sibling}) \)[/tex] is the total proportion of students with siblings, which is 0.75.
Substitute these values into the formula:
[tex]\[ P(\text{Pet} \mid \text{Sibling}) = \frac{0.3}{0.75} \][/tex]
Simplify the fraction:
[tex]\[ P(\text{Pet} \mid \text{Sibling}) = 0.4 \][/tex]
Therefore, the likelihood that a student has a pet given that he or she has a sibling is [tex]\( 0.4 \)[/tex] or [tex]\( 40\% \)[/tex].
Thus, the correct answer is:
D. [tex]\( 40 \% \)[/tex]
