Answer :
To solve the problem, we need to find the conditional probability that a student has a pet given that they have a sibling. This can be represented mathematically as [tex]\( P(\text{Pets} \mid \text{Siblings}) \)[/tex].
The table provides us with the following data:
- [tex]\( P(\text{Pets and Siblings}) = 0.3 \)[/tex]
- [tex]\( P(\text{Siblings}) = 0.75 \)[/tex]
Using the formula for conditional probability, we have:
[tex]\[ P(\text{Pets} \mid \text{Siblings}) = \frac{P(\text{Pets and Siblings})}{P(\text{Siblings})} \][/tex]
Plugging in the values, we get:
[tex]\[ P(\text{Pets} \mid \text{Siblings}) = \frac{0.3}{0.75} \][/tex]
Evaluating this expression:
[tex]\[ \frac{0.3}{0.75} = 0.4 \][/tex]
To express this probability as a percentage, we multiply by 100:
[tex]\[ 0.4 \times 100 = 40\% \][/tex]
Therefore, the likelihood that a student has a pet given that they have a sibling is [tex]\( \boxed{40\%} \)[/tex].
So, the correct answer is [tex]\( D. 40\% \)[/tex].
The table provides us with the following data:
- [tex]\( P(\text{Pets and Siblings}) = 0.3 \)[/tex]
- [tex]\( P(\text{Siblings}) = 0.75 \)[/tex]
Using the formula for conditional probability, we have:
[tex]\[ P(\text{Pets} \mid \text{Siblings}) = \frac{P(\text{Pets and Siblings})}{P(\text{Siblings})} \][/tex]
Plugging in the values, we get:
[tex]\[ P(\text{Pets} \mid \text{Siblings}) = \frac{0.3}{0.75} \][/tex]
Evaluating this expression:
[tex]\[ \frac{0.3}{0.75} = 0.4 \][/tex]
To express this probability as a percentage, we multiply by 100:
[tex]\[ 0.4 \times 100 = 40\% \][/tex]
Therefore, the likelihood that a student has a pet given that they have a sibling is [tex]\( \boxed{40\%} \)[/tex].
So, the correct answer is [tex]\( D. 40\% \)[/tex].
