Question

alexa recorded the grade-level and instrument of everyone in the middle school school of rock below.

seventh grade students

instrument	# of students
bass	10
drums	10
keyboard	2

eighth grade students

instrument	# of students
bass	8
drums	8
keyboard	6

based on these results, express the probability that a seventh grader chosen at random will play an instrument other than keyboard as a fraction in simplest form.

Explanation:

Step1: Calculate total seventh - grade students

To find the total number of seventh - grade students, we sum up the number of students for each instrument. The number of students for guitar is 13, bass is 10, drums is 10, and keyboard is 2. So the total number of seventh - grade students $N=13 + 10+10 + 2$.
$13+10 = 23$, $23+10=33$, $33 + 2=35$.

Step2: Calculate number of seventh - grade students not playing keyboard

The number of students playing keyboard is 2. So the number of students not playing keyboard is the total number of seventh - grade students minus the number of students playing keyboard. Let $n$ be the number of students not playing keyboard. Then $n=35 - 2=33$.

Step3: Calculate the probability

The probability $P$ that a randomly chosen seventh - grader does not play keyboard is the number of students not playing keyboard divided by the total number of seventh - grade students. So $P=\frac{n}{N}=\frac{33}{35}$.

Answer:

$\frac{33}{35}$