En una clase de la universidad hay 80 alumnos y 50 alumnas. La mitad de las alumnas y la mitad de los alumnos aprueban estadística. Calcula la probabilidad de que, al elegir una persona al azar, resulte ser: a) Alumna o que aprueba estadística. b) Alumno que suspenda estadística. c) Sabiendo que es alumno, ¿cuál es la probabilidad de que apruebe estadística? d) ¿Son independientes los sucesos ALUMNO y APRUEBA ESTADÍSTICA?
Hacemos la tabla de contingencia: Aprueban
Suspenden
2.
3.
Alumnos Alumnas
Aplicando la regla de Laplace obtenemos las probabilidades que nos piden:
40
25
65
80
50
130
40
25
65
a) P =
90
130
=
9
13
d) P (alumno) =
80 130
b) P = 40
130
=
P (alumno)· P(aprobar) = P(alumno ∩ aprobar) ⟹ Son independientes
Calcula la probabilidad de obtener algún 5 al lanzar un dado 3 veces. 5 6
·
5 6
·
=
5 6
=
91
216
⟹
4
13
4
13
8 = 13 ; P(aprobar)=
P (alumno ∩ aprobar) =
P (obtener algún 5) = 1 – P (no obtener ningún 5) = 1 –
40
130
65
130
=
1 2
c) P =
40 80
=
1 2
⟹ P(alumno)· P(aprobar) =
P (obtener algún 5) =
8
26
=
4
13
91
216
En una clase hay 17 chicas y se desconoce el número de chicos. Cada alumno cursa una sola optativa y se sabe que 12 estudiantes, 8 de ellos varones, eligieron música. Además, otros 8 chicos eligieron informática. Seleccionado un alumno al azar, calcula la probabilidad de que: a) Sea chico. b) Sea chica y estudie música. c) Siendo chica estudie música. Hacemos la tabla de contingencia: Chicas Chicos Aplicando la regla de Laplace: Música 4 8 12
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