To determine the likelihood that a student who has a sibling does not have a pet, we can perform the following steps:
1. Identify the given probabilities from the table:
- Probability that a student has a sibling, [tex]\( P(\text{Sibling}) \)[/tex]: 0.75
- Probability that a student has both a sibling and no pets, [tex]\( P(\text{No Pets and Sibling}) \)[/tex]: 0.45
2. Understand what is required:
- We need to find the conditional probability [tex]\( P(\text{No Pets} \mid \text{Sibling}) \)[/tex], which reads as "the probability of no pets given that the student has a sibling."
3. Apply the formula for conditional probability:
[tex]\[
P(\text{No Pets} \mid \text{Sibling}) = \frac{P(\text{No Pets and Sibling})}{P(\text{Sibling})}
\][/tex]
4. Substitute the values:
[tex]\[
P(\text{No Pets} \mid \text{Sibling}) = \frac{0.45}{0.75}
\][/tex]
5. Calculate the likelihood:
- Simplify the fraction:
[tex]\[
\frac{0.45}{0.75} = 0.6
\][/tex]
6. Convert the likelihood to a percentage:
[tex]\[
0.6 \times 100 = 60\%
\][/tex]
7. Round to the nearest whole number, if needed. In this case, 60 is already a whole number.
Therefore, the likelihood that a student who has a sibling does not have a pet is [tex]\( \boxed{60\%} \)[/tex].
Given the answer choices:
A. About [tex]\( 82 \% \)[/tex]
B. [tex]\( 45 \% \)[/tex]
C. [tex]\( 40 \% \)[/tex]
D. [tex]\( 60 \% \)[/tex]
The correct answer is [tex]\( \boxed{60 \%} \)[/tex].
