To solve this problem, we need to calculate the conditional probability that a student has a pet given that they do not have any siblings. This can be approached step by step as follows:
1. Identify the relevant probabilities from the table:
- The probability that a student has pets and no siblings is given by the relative frequency [tex]\( \text{P}(\text{Pets and No Siblings}) \)[/tex]. From the table, this value is [tex]\( 0.15 \)[/tex].
- The probability that a student has no siblings is given by the relative frequency [tex]\( \text{P}(\text{No Siblings}) \)[/tex]. From the table, this value is [tex]\( 0.25 \)[/tex].
2. Use the definition of conditional probability:
The conditional probability of having pets given that a student has no siblings is defined as:
[tex]\[
\text{P}(\text{Pets}|\text{No Siblings}) = \frac{\text{P}(\text{Pets and No Siblings})}{\text{P}(\text{No Siblings})}
\][/tex]
3. Substitute the probabilities into the formula:
[tex]\[
\text{P}(\text{Pets}|\text{No Siblings}) = \frac{0.15}{0.25}
\][/tex]
4. Calculate the conditional probability:
[tex]\[
\text{P}(\text{Pets}|\text{No Siblings}) = \frac{0.15}{0.25} = 0.6
\][/tex]
5. Convert the probability into a percentage:
[tex]\[
0.6 \times 100 = 60\%
\][/tex]
Therefore, the likelihood that a student who does not have any siblings has a pet is [tex]\( 60\% \)[/tex].
The correct answer is:
A. [tex]\( 60\% \)[/tex]
