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Latanya recorded the grade-level and instrument of everyone in the middle school School of Rock below.Seventh Grade StudentsInstrument # of StudentsGuitar 2Bass 2Drums 11Keyboard 15Eighth Grade StudentsInstrument # of StudentsGuitar 6Bass 15Drums 10Keyboard 9Based on these results, express the probability that an eighth grader chosen at random will play the keyboard as a fraction in simplest form.

Question

Latanya recorded the grade-level and instrument of everyone in the middle school School of Rock below.Seventh Grade StudentsInstrument # of StudentsGuitar 2Bass 2Drums 11Keyboard 15Eighth Grade StudentsInstrument # of StudentsGuitar 6Bass 15Drums 10Keyboard 9Based on these results, express the probability that an eighth grader chosen at random will play the keyboard as a fraction in simplest form.

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Solution

To find the probability that an eighth grader chosen at random will play the keyboard, we need to know the total number of eighth graders and the number of eighth graders who play the keyboard.

From the data given, we know that:

  • The number of eighth graders who play the guitar is 6.
  • The number of eighth graders who play the bass is 15.
  • The number of eighth graders who play the drums is 10.
  • The number of eighth graders who play the keyboard is 9.

So, the total number of eighth graders is 6 (guitar) + 15 (bass) + 10 (drums) + 9 (keyboard) = 40 students.

The probability of an event is calculated as the number of favorable outcomes divided by the total number of outcomes. In this case, the favorable outcome is an eighth grader who plays the keyboard, and the total number of outcomes is the total number of eighth graders.

So, the probability that an eighth grader chosen at random will play the keyboard is 9 (the number of eighth graders who play the keyboard) divided by 40 (the total number of eighth graders).

Therefore, the probability is 9/40. This fraction is already in its simplest form, so the final answer is 9/40.

This problem has been solved

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