First, we need to calculate the total number of students in both grades and the total number of students who play bass.
Seventh Grade Students:
- Guitar: 9
- Bass: 8
- Drums: 11
- Keyboard: 11
Total for seventh grade: \[ 9 + 8 + 11 + 11 = 39 \]
Eighth Grade Students:
- Guitar: 9
- Bass: 4
- Drums: 11
- Keyboard: 14
Total for eighth grade: \[ 9 + 4 + 11 + 14 = 38 \]
Now, we find the total number of students in the middle school: \[ 39 + 38 = 77 \]
Next, we calculate the total number of students who play the bass:
- Seventh grade: 8
- Eighth grade: 4
Total students who play bass: \[ 8 + 4 = 12 \]
Now we can find the probability that a randomly chosen student plays the bass: \[ \text{Probability} = \frac{\text{Number of students who play bass}}{\text{Total number of students}} = \frac{12}{77} \]
The fraction \( \frac{12}{77} \) is already in simplest form, as 12 and 77 have no common factors other than 1.
The probability that a student chosen at random will play the bass is: \[ \frac{12}{77} \]