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To determine the experimental probability that a randomly chosen 10th-grade student has at least one, but no more than two, siblings, let's follow these steps:
1. Identify the total number of students surveyed:
We add up the number of students in each sibling category:
- Students with 0 siblings: 4
- Students with 1 sibling: 18
- Students with 2 siblings: 10
- Students with 3 siblings: 8
Adding these together gives us:
[tex]\[ 4 + 18 + 10 + 8 = 40 \][/tex]
So, the total number of students surveyed is 40.
2. Identify the number of students with at least one, but no more than two, siblings:
We focus on students with either 1 or 2 siblings:
- Students with 1 sibling: 18
- Students with 2 siblings: 10
Adding these together gives us:
[tex]\[ 18 + 10 = 28 \][/tex]
So, the number of students with at least one, but no more than two, siblings is 28.
3. Calculate the experimental probability:
The experimental probability is obtained by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, it is the proportion of students with at least one, but no more than two, siblings out of the total number of students:
[tex]\[ \text{Probability} = \frac{\text{Number of students with 1 or 2 siblings}}{\text{Total number of students}} = \frac{28}{40} \][/tex]
Simplifying this fraction:
[tex]\[ \frac{28}{40} = 0.7 \][/tex]
4. Convert the probability to a percentage:
To convert a probability to a percentage, we multiply by 100:
[tex]\[ 0.7 \times 100 = 70\% \][/tex]
5. Round to the nearest whole percent (if necessary):
In this case, 70% is already a whole number, so no rounding is necessary.
Therefore, the experimental probability that a randomly chosen 10th-grade student has at least one but no more than two siblings is [tex]\(70\%\)[/tex]. The correct answer is:
[tex]\[ \boxed{70\%} \][/tex]
1. Identify the total number of students surveyed:
We add up the number of students in each sibling category:
- Students with 0 siblings: 4
- Students with 1 sibling: 18
- Students with 2 siblings: 10
- Students with 3 siblings: 8
Adding these together gives us:
[tex]\[ 4 + 18 + 10 + 8 = 40 \][/tex]
So, the total number of students surveyed is 40.
2. Identify the number of students with at least one, but no more than two, siblings:
We focus on students with either 1 or 2 siblings:
- Students with 1 sibling: 18
- Students with 2 siblings: 10
Adding these together gives us:
[tex]\[ 18 + 10 = 28 \][/tex]
So, the number of students with at least one, but no more than two, siblings is 28.
3. Calculate the experimental probability:
The experimental probability is obtained by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, it is the proportion of students with at least one, but no more than two, siblings out of the total number of students:
[tex]\[ \text{Probability} = \frac{\text{Number of students with 1 or 2 siblings}}{\text{Total number of students}} = \frac{28}{40} \][/tex]
Simplifying this fraction:
[tex]\[ \frac{28}{40} = 0.7 \][/tex]
4. Convert the probability to a percentage:
To convert a probability to a percentage, we multiply by 100:
[tex]\[ 0.7 \times 100 = 70\% \][/tex]
5. Round to the nearest whole percent (if necessary):
In this case, 70% is already a whole number, so no rounding is necessary.
Therefore, the experimental probability that a randomly chosen 10th-grade student has at least one but no more than two siblings is [tex]\(70\%\)[/tex]. The correct answer is:
[tex]\[ \boxed{70\%} \][/tex]
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