Questions: Arturo recorded the grade-level and instrument of everyone in the middle school School of Rock below. Seventh Grade Students Instrument # of Students Guitar 4 Bass 5 Drums 3 Keyboard 5 Eighth Grade Students Instrument # of Students Guitar 6 Bass 8 Drums 2 Keyboard 15 Based on these results, express the probability that a student chosen at random will play the guitar as a fraction in simplest form.

Solution Steps

First, we need to calculate the total number of students in both the seventh and eighth grades.

• Seventh Grade Students:

  • Guitar: 4
  • Bass: 5
  • Drums: 3
  • Keyboard: 5

  Total for seventh grade: \(4 + 5 + 3 + 5 = 17\)

• Eighth Grade Students:

  • Guitar: 6
  • Bass: 8
  • Drums: 2
  • Keyboard: 15

  Total for eighth grade: \(6 + 8 + 2 + 15 = 31\)

• Total Students:

  • Total number of students = \(17 + 31 = 48\)

Next, we calculate the total number of students who play the guitar.

• Seventh Grade Guitar Players: 4

• Eighth Grade Guitar Players: 6

• Total Guitar Players: \(4 + 6 = 10\)

Now, we calculate the probability that a randomly chosen student plays the guitar. This is the ratio of the number of guitar players to the total number of students.

\[ \text{Probability} = \frac{\text{Total Guitar Players}}{\text{Total Students}} = \frac{10}{48} \]

Simplify the fraction:

\[ \frac{10}{48} = \frac{5}{24} \]

Final Answer