Final answer:
The probability that an eighth grader chosen at random will play an instrument other than keyboard can be expressed as 31/42.
Step-by-step explanation:
To find the probability that an eighth grader chosen at random will play an instrument other than keyboard, we need to calculate the number of eighth graders playing instruments other than keyboard and divide it by the total number of eighth graders.
From the data provided, we know that there are 8 eighth-grade students playing bass, 11 playing guitar, and 12 playing drums.
Therefore, the total number of eighth graders playing instruments other than keyboard is 8 + 11 + 12 = 31.
The total number of eighth graders is given as 8 + 11 + 12 + 11 = 42.
So, the probability can be expressed as 31/42, which is the fraction in simplest form.