To determine the likelihood that a student who has a sibling does not have a pet, we need to analyze the given relative frequency table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \text{Siblings} & \text{No siblings} & \text{Total} \\
\hline \text{Pets} & 0.3 & 0.15 & 0.45 \\
\hline \text{No pets} & 0.45 & 0.1 & 0.55 \\
\hline \text{Total} & 0.75 & 0.25 & 1.0 \\
\hline
\end{tabular}
\][/tex]
Let's break down the steps:
1. Identify the probability that a student does not have a pet given that they have a sibling.
From the table:
- The probability that a student has siblings and no pets is 0.45.
- The total probability that a student has siblings (regardless of pets) is 0.75.
2. Use the conditional probability formula:
[tex]\[
P(\text{No pets} \mid \text{Siblings}) = \frac{P(\text{Siblings and No pets})}{P(\text{Siblings})}
\][/tex]
3. Substitute the values from the table:
[tex]\[
P(\text{No pets} \mid \text{Siblings}) = \frac{0.45}{0.75}
\][/tex]
4. Simplify the fraction:
[tex]\[
P(\text{No pets} \mid \text{Siblings}) = \frac{0.45}{0.75} = 0.6
\][/tex]
5. Convert the result to a percentage:
[tex]\[
0.6 \times 100 = 60\%
\][/tex]
So, the likelihood that a student with siblings does not have a pet is [tex]\(\boxed{60\%}\)[/tex].
Therefore, the correct answer is:
B. [tex]\(60 \% \)[/tex]
