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

\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 also has a pet?

A. [tex]$75 \%$[/tex]
B. [tex]$30 \%$[/tex]
C. About [tex]$67 \%$[/tex]
D. [tex]$40 \%$[/tex]



Answer :

To solve the problem, we need to find the conditional probability that a student has a pet given that they have a sibling. This can be represented mathematically as [tex]\( P(\text{Pets} \mid \text{Siblings}) \)[/tex].

The table provides us with the following data:
- [tex]\( P(\text{Pets and Siblings}) = 0.3 \)[/tex]
- [tex]\( P(\text{Siblings}) = 0.75 \)[/tex]

Using the formula for conditional probability, we have:
[tex]\[ P(\text{Pets} \mid \text{Siblings}) = \frac{P(\text{Pets and Siblings})}{P(\text{Siblings})} \][/tex]

Plugging in the values, we get:
[tex]\[ P(\text{Pets} \mid \text{Siblings}) = \frac{0.3}{0.75} \][/tex]

Evaluating this expression:
[tex]\[ \frac{0.3}{0.75} = 0.4 \][/tex]

To express this probability as a percentage, we multiply by 100:
[tex]\[ 0.4 \times 100 = 40\% \][/tex]

Therefore, the likelihood that a student has a pet given that they have a sibling is [tex]\( \boxed{40\%} \)[/tex].

So, the correct answer is [tex]\( D. 40\% \)[/tex].