Certainly! Let's dissect the given problem using the relative frequency table provided:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline & \text{Siblings} & \text{No siblings} & \text{Total} \\
\hline \text{Pets} & 0.3 & 0.15 & 0.45 \\
\hline \text{No pets} & 0.45 & 0.1 & 0.55 \\
\hline \text{Total} & 0.75 & 0.25 & 1.0 \\
\hline
\end{array}
\][/tex]
The question asks for the probability that a student does not have a pet given that they have a sibling.
### Step-by-Step Solution:
1. Identify Relevant Probabilities from the Table:
- The probability that a student has siblings and no pets is given as \(0.45\).
- The probability that a student has siblings (regardless of pet status) is given as \(0.75\).
2. Apply Conditional Probability Formula:
- The conditional probability formula for our context is:
[tex]\[
P(\text{No pets} \mid \text{Siblings}) = \frac{P(\text{No pets and Siblings})}{P(\text{Siblings})}
\][/tex]
- Substituting the values from the table:
[tex]\[
P(\text{No pets} \mid \text{Siblings}) = \frac{P(\text{No pets and Siblings})}{P(\text{Siblings})} = \frac{0.45}{0.75}
\][/tex]
3. Calculate the Probability:
- Performing the division:
[tex]\[
P(\text{No pets} \mid \text{Siblings}) = \frac{0.45}{0.75} = 0.6
\][/tex]
4. Convert to a Percentage:
- To express this probability as a percentage:
[tex]\[
0.6 \times 100\% = 60\%
\][/tex]
Thus, the likelihood that a student does not have a pet given that he or she has a sibling is \(60\%\).
### Answer:
The correct answer is [tex]\( \boxed{60\%} \)[/tex]. This corresponds to option D.
