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:

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.

$$ \frac{68}{107} \approx 0.6355 $$

$$ 0.6355 \times 100\% \approx 64\% $$

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>%