Julieta recorded the grade-level and instrument of everyone in the middle school School of Rock below.Seventh Grade StudentsInstrument # of StudentsGuitar 12Bass 3Drums 10Keyboard 5Eighth Grade StudentsInstrument # of StudentsGuitar 4Bass 3Drums 6Keyboard 2Based on these results, express the probability that a student chosen at random will play an instrument other than guitar as a fraction in simplest form.
Question
Julieta recorded the grade-level and instrument of everyone in the middle school School of Rock below.Seventh Grade StudentsInstrument # of StudentsGuitar 12Bass 3Drums 10Keyboard 5Eighth Grade StudentsInstrument # of StudentsGuitar 4Bass 3Drums 6Keyboard 2Based on these results, express the probability that a student chosen at random will play an instrument other than guitar as a fraction in simplest form.
Solution
To solve this problem, we first need to find the total number of students and the number of students who play guitar.
From the data, we can see that:
- The number of 7th grade students who play guitar is 12.
- The number of 8th grade students who play guitar is 4.
So, the total number of students who play guitar is 12 + 4 = 16.
Next, we find the total number of students:
- The number of 7th grade students is 12 (guitar) + 3 (bass) + 10 (drums) + 5 (keyboard) = 30.
- The number of 8th grade students is 4 (guitar) + 3 (bass) + 6 (drums) + 2 (keyboard) = 15.
So, the total number of students is 30 + 15 = 45.
The probability that a student chosen at random will play an instrument other than guitar is the number of students who do not play guitar divided by the total number of students.
The number of students who do not play guitar is the total number of students minus the number of students who play guitar, which is 45 - 16 = 29.
So, the probability is 29/45. This fraction is already in its simplest form, so the final answer is 29/45.
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