Question

in a group of students, 27 play soccer, 39 play basketball, and 41 run track. what is the probability that a randomly selected student doesnt play basketball?

\\(p(\text{not in basketball}) = \quad\\%\\)

round your answer to the nearest whole percent.

Explanation:

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<reasoning>

Determine the sample space size

We find the total number of students in the group.
Using the Sample Space knowledge point:
\[
\text{Total} = 27 + 39 + 41 = 107
\]

Find the number of students not playing basketball

We calculate how many students do not play basketball.
Using the Complementary Probability knowledge point:
\[
\text{Not Basketball} = 107 - 39 = 68
\]

Calculate the probability

We find the probability as a fraction.
Using the Theoretical Probability knowledge point:
\[
P(\text{not in basketball}) = \frac{68}{107}
\]

Convert to a percentage

We convert the fraction to a percentage and round to the nearest whole percent.
\[
\frac{68}{107} \approx 0.6355
\]
\[
0.6355 \times 100\% \approx 64\%
\]
</reasoning>

<answer>
In a group of students, 27 play soccer, 39 play basketball, and 41 run track. What is the probability that a randomly selected student doesn't play basketball?

\(P(\text{not in basketball}) =\) <blank>64</blank>%
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Statistics",
"Complementary Probability"
]
}
</post_analysis>

Answer:

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<reasoning>

Determine the sample space size

We find the total number of students in the group.
Using the Sample Space knowledge point:
\[
\text{Total} = 27 + 39 + 41 = 107
\]

Find the number of students not playing basketball

We calculate how many students do not play basketball.
Using the Complementary Probability knowledge point:
\[
\text{Not Basketball} = 107 - 39 = 68
\]

Calculate the probability

We find the probability as a fraction.
Using the Theoretical Probability knowledge point:
\[
P(\text{not in basketball}) = \frac{68}{107}
\]

Convert to a percentage

We convert the fraction to a percentage and round to the nearest whole percent.
\[
\frac{68}{107} \approx 0.6355
\]
\[
0.6355 \times 100\% \approx 64\%
\]
</reasoning>

<answer>
In a group of students, 27 play soccer, 39 play basketball, and 41 run track. What is the probability that a randomly selected student doesn't play basketball?

\(P(\text{not in basketball}) =\) <blank>64</blank>%
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Statistics",
"Complementary Probability"
]
}
</post_analysis>