The table shows the results of a survey in which 10th-grade students were asked how many siblings (brothers and/or sisters) they have.

\begin{tabular}{|c|c|}
\hline \begin{tabular}{c}
Number of \\
Siblings
\end{tabular} & \begin{tabular}{c}
Number of \\
Students
\end{tabular} \\
\hline 0 & 4 \\
\hline 1 & 18 \\
\hline 2 & 10 \\
\hline 3 & 8 \\
\hline
\end{tabular}

What is the experimental probability that a 10th-grade student chosen at random has at least one, but no more than two, siblings? Round to the nearest whole percent.

A. [tex]$65 \%$[/tex]

B. [tex]$70 \%$[/tex]

C. [tex]$75 \%$[/tex]

D. [tex]$80 \%$[/tex]



Answer :

To solve this problem, follow these steps:

1. Count the number of students with at least one, but no more than two, siblings:
- Students with 1 sibling: [tex]\(18\)[/tex]
- Students with 2 siblings: [tex]\(10\)[/tex]

Add these two numbers together to find the total number of students with at least one, but no more than two, siblings:
[tex]\[ 18 + 10 = 28 \][/tex]

2. Calculate the total number of students surveyed:
Add the numbers of students in each category:
- Students with 0 siblings: [tex]\(4\)[/tex]
- Students with 1 sibling: [tex]\(18\)[/tex]
- Students with 2 siblings: [tex]\(10\)[/tex]
- Students with 3 siblings: [tex]\(8\)[/tex]

So, the total number of students is:
[tex]\[ 4 + 18 + 10 + 8 = 40 \][/tex]

3. Determine the experimental probability:
The probability is the ratio of the number of students with at least one, but no more than two, siblings to the total number of students. Therefore, the probability is:
[tex]\[ \frac{28}{40} \][/tex]

Convert this fraction to a percentage by multiplying by 100:
[tex]\[ \left(\frac{28}{40}\right) \times 100 = 70\% \][/tex]

4. Round the result to the nearest whole percent:
The probability is already a whole number, so no further rounding is needed.

Therefore, the experimental probability that a 10th-grade student chosen at random has at least one, but no more than two, siblings is:
[tex]\[ \boxed{70\%} \][/tex]

So, the correct answer is [tex]\(70\%\)[/tex].