To determine the likelihood that a student with siblings also has a pet, we are essentially looking for the conditional probability [tex]\( P(\text{Pet} \mid \text{Siblings}) \)[/tex].
Given:
- [tex]\( P(\text{Siblings}) = 0.75 \)[/tex] (The proportion of students with siblings)
- [tex]\( P(\text{Pet} \cap \text{Siblings}) = 0.30 \)[/tex] (The proportion of students who have both siblings and pets)
The conditional probability [tex]\( P(\text{Pet} \mid \text{Siblings}) \)[/tex] is calculated as:
[tex]\[ P(\text{Pet} \mid \text{Siblings}) = \frac{P(\text{Pet} \cap \text{Siblings})}{P(\text{Siblings})} \][/tex]
Plugging in the given values:
[tex]\[ P(\text{Pet} \mid \text{Siblings}) = \frac{0.30}{0.75} \][/tex]
Now, performing the division:
[tex]\[ P(\text{Pet} \mid \text{Siblings}) = 0.4 \][/tex]
Thus, the likelihood that a student with siblings also has a pet is 40%, which corresponds to option B.
So, the correct answer is:
B. [tex]\( 40 \% \)[/tex]
