To determine the experimental probability that a randomly chosen 10th-grade student has at least one, but no more than two, siblings, let's go through the steps in detail:
1. Total Number of Students:
The first step is to calculate the total number of students surveyed. This can be done by adding the number of students in each category:
[tex]\[
4 \, (\text{students with 0 siblings}) + 18 \, (\text{students with 1 sibling}) + 10 \, (\text{students with 2 siblings}) + 8 \, (\text{students with 3 siblings})
\][/tex]
[tex]\[
4 + 18 + 10 + 8 = 40 \text{ students}
\][/tex]
2. Number of Students with 1 or 2 Siblings:
Next, we need to determine how many students have either 1 or 2 siblings. This can be done by adding the number of students who have exactly 1 sibling to the number of students who have exactly 2 siblings:
[tex]\[
18 \, (\text{students with 1 sibling}) + 10 \, (\text{students with 2 siblings})
\][/tex]
[tex]\[
18 + 10 = 28 \text{ students}
\][/tex]
3. Calculate the Experimental Probability:
To find the experimental probability, we take the number of students who have at least one, but no more than two, siblings, and divide it by the total number of students. Then we multiply the result by 100 to convert the probability into a percentage:
[tex]\[
\frac{28}{40} \times 100 = 70\%
\][/tex]
4. Round to the Nearest Whole Percent:
The calculation yields an exact figure of 70%, so rounding to the nearest whole percent does not change the number.
Therefore, the experimental probability that a randomly chosen 10th-grade student has at least one, but no more than two, siblings is [tex]\(\boxed{70\%}\)[/tex].
