Aria recorded the grade-level and instrument of everyone in the middle school School of Rock below.Seventh Grade StudentsInstrument # of StudentsGuitar 13Bass 9Drums 3Keyboard 6Eighth Grade StudentsInstrument # of StudentsGuitar 14Bass 15Drums 6Keyboard 5Based on these results, express the probability that an eighth grader chosen at random will play an instrument other than bass as a fraction in simplest form.
Question
Aria recorded the grade-level and instrument of everyone in the middle school School of Rock below.Seventh Grade StudentsInstrument # of StudentsGuitar 13Bass 9Drums 3Keyboard 6Eighth Grade StudentsInstrument # of StudentsGuitar 14Bass 15Drums 6Keyboard 5Based on these results, express the probability that an eighth grader chosen at random will play an instrument other than bass as a fraction in simplest form.
Solution 1
Primero, necesitamos determinar el número total de estudiantes de octavo grado. Sumamos el número de estudiantes que tocan cada instrumento:
Guitarra: 14 Bajo: 15 Batería: 6 Teclado: 5
Total de estudiantes de octavo grado = 14 + 15 + 6 + 5 = 40
Luego, encontramos el número de estudiantes de octavo grado que tocan un instrumento que no sea el bajo. Sumamos el número de estudiantes que tocan guitarra, batería y teclado:
Guitarra: 14 Batería: 6 Teclado: 5
Total de estudiantes que no tocan bajo = 14 + 6 + 5 = 25
Ahora, la probabilidad de que un estudiante de octavo grado elegido al azar toque un instrumento que no sea el bajo es el número de estudiantes que no tocan bajo dividido por el número total de estudiantes de octavo grado:
Probabilidad = 25 / 40
Simplificamos la fracción dividiendo el numerador y el denominador por su máximo común divisor, que es 5:
25 ÷ 5 = 5 40 ÷ 5 = 8
Por lo tanto, la probabilidad en su forma más simple es 5/8.
Solution 2
First, let's find the total number of eighth grade students.
The number of eighth grade students playing guitar is 14, bass is 15, drums is 6, and keyboard is 5.
So, the total number of eighth grade students is 14 (guitar) + 15 (bass) + 6 (drums) + 5 (keyboard) = 40 students.
The question asks for the probability that an eighth grader chosen at random will play an instrument other than bass.
The number of students who play an instrument other than bass is the total number of students minus the number of students who play bass.
So, the number of students who play an instrument other than bass is 40 (total students) - 15 (bass players) = 25 students.
The probability of an event is the number of ways that event can occur divided by the total number of outcomes.
So, the probability that an eighth grader chosen at random will play an instrument other than bass is 25 (students who play an instrument other than bass) / 40 (total students).
This simplifies to 5/8.
So, the probability that an eighth grader chosen at random will play an instrument other than bass is 5/8.
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