To determine the probability that a randomly chosen student plays the bass, we first need to calculate the total number of students in the middle school School of Rock.
Seventh Grade Students:
- Guitar: 12
- Bass: 14
- Drums: 5
- Keyboard: 4
Total for Seventh Grade = 12 + 14 + 5 + 4 = 35 students
Eighth Grade Students:
- Guitar: 9
- Bass: 10
- Drums: 3
- Keyboard: 6
Total for Eighth Grade = 9 + 10 + 3 + 6 = 28 students
Grand Total of Students: Total number of students = Total Seventh Grade + Total Eighth Grade = 35 + 28 = 63 students
Number of bass players:
- Seventh Grade Bass Players: 14
- Eighth Grade Bass Players: 10 Total Bass Players = 14 + 10 = 24
Now, the probability \( P \) that a randomly chosen student plays the bass is given by the formula:
\[ P(\text{Bass}) = \frac{\text{Number of Bass Players}}{\text{Total Number of Students}} = \frac{24}{63} \]
Next, we need to simplify the fraction \( \frac{24}{63} \). Both numbers can be divided by their greatest common divisor (GCD), which is 3:
\[ \frac{24 \div 3}{63 \div 3} = \frac{8}{21} \]
Thus, the probability that a student chosen at random will play the bass is:
\[ \boxed{\frac{8}{21}} \]