n a class of 30 students, 8 have a brother and 12 have a sister. There are 3 students who have a brother and a sister. What is the probability that a student who has a brother also has a sister?
Question
n a class of 30 students, 8 have a brother and 12 have a sister. There are 3 students who have a brother and a sister. What is the probability that a student who has a brother also has a sister?
Solution
Para resolver esta pregunta, sigamos los siguientes pasos:
-
Identificar las variables y datos dados:
- Total de estudiantes en la clase: 30
- Estudiantes con un hermano: 8
- Estudiantes con una hermana: 12
- Estudiantes con un hermano y una hermana: 3
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Determinar el número de estudiantes que tienen solo un hermano:
- Estudiantes con solo un hermano = Estudiantes con un hermano - Estudiantes con un hermano y una hermana
- Estudiantes con solo un hermano = 8 - 3 = 5
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Determinar el número de estudiantes que tienen solo una hermana:
- Estudiantes con solo una hermana = Estudiantes con una hermana - Estudiantes con un hermano y una hermana
- Estudiantes con solo una hermana = 12 - 3 = 9
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Determinar el número de estudiantes que tienen un hermano y una hermana:
- Ya sabemos que son 3 estudiantes.
-
Calcular la probabilidad de que un estudiante que tiene un hermano también tenga una hermana:
- La probabilidad se calcula como el número de estudiantes que tienen un hermano y una hermana dividido por el número total de estudiantes que tienen un hermano.
- Probabilidad = (Número de estudiantes con un hermano y una hermana) / (Número de estudiantes con un hermano)
- Probabilidad = 3 / 8
Por lo tanto, la probabilidad de que un estudiante que tiene un hermano también tenga una hermana es o 0.375.
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