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A survey asked students whether they have any siblings and pets. The survey data are shown in the relative frequency table below:

\begin{tabular}{|c|c|c|c|}
\hline & Siblings & No siblings & Total \\
\hline Pets & 0.3 & 0.15 & 0.45 \\
\hline No pets & 0.45 & 0.1 & 0.55 \\
\hline Total & 0.75 & 0.25 & 1.0 \\
\hline
\end{tabular}

Given that a student has a sibling, what is the likelihood that he or she does not have a pet?

A. About [tex]$82\%$[/tex]
B. [tex]$45\%$[/tex]
C. [tex]$40\%$[/tex]
D. [tex]$60\%$[/tex]



Answer :

GinnyAnswer
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].

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