Question

In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the class plays a sport?
Plays an instrument Does not play an instrument
Plays a sport 6 8
Does not play a sport 13 3
Answer
Attempt 2 out of 2

Answer 1

To find the probability that a randomly chosen student plays a sport, we need to determine the total number of students and the number of students who play a sport.

From the data table:

- Students who play a sport and play an instrument: 6
- Students who play a sport and do not play an instrument: 8

So, the total number of students who play a sport is:

\[
6 + 8 = 14
\]

Next, we can find the total number of students in the class by adding all categories together:

- Students who play a sport and play an instrument: 6
- Students who play a sport and do not play an instrument: 8
- Students who do not play a sport but play an instrument: 13
- Students who do not play a sport and do not play an instrument: 3

Calculating the total:

\[
6 + 8 + 13 + 3 = 30
\]

Now we can find the probability that a randomly chosen student plays a sport:

\[
P(\text{plays a sport}) = \frac{\text{Number of students who play a sport}}{\text{Total number of students}} = \frac{14}{30}
\]

We can simplify the fraction:

\[
\frac{14}{30} = \frac{7}{15}
\]

Thus, the probability that a randomly chosen student plays a sport is:

\[
\frac{7}{15}
\]