Question

in a group of students, 61 play soccer, 56 play basketball, and 72 run track.
what is the probability that a randomly selected student doesnt run track?
\\(p(\text{doesnt run track}) = \\ ?\\ \\%\\)
round your answer to the nearest whole percent.

Explanation:

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<reasoning>

Calculate total students

We find the total number of students in the group.
Using the Theoretical Probability knowledge point:
\[
\text{Total} = 61 + 56 + 72 = 189
\]

Find students not running track

We find the number of students who do not run track.
Using the Complementary Probability knowledge point:
\[
\text{Not Track} = 189 - 72 = 117
\]

Calculate the probability

We compute the probability as a fraction.
Using the Theoretical Probability knowledge point:
\[
P(\text{doesn't run track}) = \frac{117}{189}
\]

Convert to percentage

We convert the fraction to a percentage.
\[
\frac{117}{189} \approx 0.619047
\]
\[
0.619047 \times 100\% \approx 61.9\%
\]

Round to nearest whole percent

We round the percentage to the nearest integer.
\[
61.9\% \approx 62\%
\]
</reasoning>

<answer>
In a group of students, 61 play soccer, 56 play basketball, and 72 run track. What is the probability that a randomly selected student doesn't run track?

\(P(\text{doesn't run track}) =\) <blank>62</blank>%

Round your answer to the nearest whole percent.
</answer>

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

Answer:

<pre_analysis>
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<reasoning>

Calculate total students

We find the total number of students in the group.
Using the Theoretical Probability knowledge point:
\[
\text{Total} = 61 + 56 + 72 = 189
\]

Find students not running track

We find the number of students who do not run track.
Using the Complementary Probability knowledge point:
\[
\text{Not Track} = 189 - 72 = 117
\]

Calculate the probability

We compute the probability as a fraction.
Using the Theoretical Probability knowledge point:
\[
P(\text{doesn't run track}) = \frac{117}{189}
\]

Convert to percentage

We convert the fraction to a percentage.
\[
\frac{117}{189} \approx 0.619047
\]
\[
0.619047 \times 100\% \approx 61.9\%
\]

Round to nearest whole percent

We round the percentage to the nearest integer.
\[
61.9\% \approx 62\%
\]
</reasoning>

<answer>
In a group of students, 61 play soccer, 56 play basketball, and 72 run track. What is the probability that a randomly selected student doesn't run track?

\(P(\text{doesn't run track}) =\) <blank>62</blank>%

Round your answer to the nearest whole percent.
</answer>

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