To solve the problem of determining the likelihood that a student who does not have siblings has a pet, we can use the concept of conditional probability. Here’s a step-by-step explanation:
1. Identify the Given Data:
- Probability of having no siblings (P(No siblings)): This is the total proportion of students with no siblings, which is 0.25.
- Probability of having no siblings and having a pet (P(Pets and No siblings)): This is the joint probability, which is 0.15.
2. Formulate the Problem Using Conditional Probability:
- We want to find [tex]\( P(\text{Pets} \mid \text{No siblings}) \)[/tex], which reads as the probability that a student has a pet given that they have no siblings.
3. Apply the Conditional Probability Formula:
- Conditional probability can be defined as:
[tex]\[
P(\text{Pets} \mid \text{No siblings}) = \frac{P(\text{Pets and No siblings})}{P(\text{No siblings})}
\][/tex]
4. Substitute the Given Values:
- [tex]\( P(\text{Pets and No siblings}) = 0.15 \)[/tex]
- [tex]\( P(\text{No siblings}) = 0.25 \)[/tex]
- Therefore,
[tex]\[
P(\text{Pets} \mid \text{No siblings}) = \frac{0.15}{0.25}
\][/tex]
5. Calculate the Result:
- [tex]\( \frac{0.15}{0.25} = 0.6 \)[/tex]
6. Convert the Probability to a Percentage:
- Since probabilities can also be expressed as percentages, we multiply by 100 to get the percentage:
[tex]\[
0.6 \times 100 = 60\%
\][/tex]
The likelihood that a student who does not have siblings has a pet is [tex]\(60\%\)[/tex].
Therefore, the correct answer to the question is:
D. 60%
