Question

Isaiah recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 11
Bass 3
Drums 3
Keyboard 4
Eighth Grade Students
Instrument # of Students
Guitar 4
Bass 10
Drums 6
Keyboard 3

Based on these results, express the probability that an eighth grader chosen at random will play the guitar as a decimal to the nearest hundredth.

Answer 1

To find the probability that an eighth grader chosen at random plays the guitar, we need to determine the total number of eighth graders and the number of eighth graders who play the guitar.

From the data provided for eighth grade students:

- Guitar: 4
- Bass: 10
- Drums: 6
- Keyboard: 3

First, we calculate the total number of eighth graders:

\[
\text{Total eighth graders} = 4 + 10 + 6 + 3 = 23
\]

Next, we focus on those who play guitar. There are 4 eighth graders that play the guitar.

Now we can calculate the probability \( P \) that an eighth grader chosen at random plays the guitar:

\[
P(\text{guitar}) = \frac{\text{Number of eighth graders playing guitar}}{\text{Total number of eighth graders}} = \frac{4}{23}
\]

Next, we need to convert this fraction into a decimal.

Calculating \( \frac{4}{23} \):

\[
\frac{4}{23} \approx 0.17391304347826086
\]

Rounding this to the nearest hundredth gives us:

\[
0.17
\]

Thus, the probability that an eighth grader chosen at random will play the guitar is:

\[
\boxed{0.17}
\]