Ejercicios de probabilidad

PROBABILIDAD

ACTIVIDAD No. 1

CONJUNTOS Y EXPERIMENTOS ALEATORIOS

PRESENTADO POR:

FANNY PATRICIA CARREÑO DEVIA

CODIGO: 40316969

PRESENTADO A:

VLADIMIR GUTIERREZ

TUTOR

UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIA “UNAD”

ESCUELA DE CIENCIAS AGRARIAS, PECUARIAS Y DEL MEDIO AMBIENTE

PROGRAMA DE ZOOTECNIA

CEAD ACACIAS

MARZO

2011

ACTIVIDAD

CONJUNTOS

1.Sea A el Conjunto de los números naturales entre 7 y 25 que son pares.

Describir A de acuerdo al:

a. Método de extensión
b. Método de comprensión

Rta:

a. Método de extensión

A = {8, 10, 12, 14, 16, 18, 20, 22, 24}

b. Método de comprensión

A = {x/x son los #s naturales pares entre 7 y 25}

2. Sea A = {x/x2 – 3x + 2 = 0}, B = {x/x2 _ 16}. Determinar si A ( Bo no

Rta: si A ( B

x2 – 3x + 2 = 0
(x - 2) (x - 1) = 0
x – 2 = 0 x – 1 = 0
x = 2 x = 1

A = {1, 2}

x2 = ( 16
x2 – 16 ( 0

(x – 4) (x + 4) ( 0

x – 4 ( 0 ( x + 4 ( 0 V x – 4 ( 0 ( x + 4 ( 0
x ( 4 ( x ( -4 x ( 4 ( x ( -4
{(} {-4, 4}

B = {-4, 4}

A ( B

OPERACIONES ENTRE CONJUNTOS Y DIAGRAMAS DE VENN

2. Sea un universo U = {1, 2, 3, 4, 5}y supóngase que los subconjuntos de U son:

A = {1,5}, B = {2, 3, 5} C = {4, 2}. Encontrar:

a. A ( (B ( C)
b. (A ( B) ( C
c. A ( (B ( C)
d. (A ( B) ( (A ( C)
e. A’ ( (B’ ( C’)
f. (A ( B) – (A ( C)
g. (A ( C)’ ( B
h. A – (B’ ( C’)

Rta:
a. A ( (B ( C)

B ( C = {2, 3, 4, 5}
A ( (B ( C) = {1, 2, 3, 4, 5}

b. (A ( B) ( C

A ( B = {1, 2, 3, 5}(A ( B) ( C = {1, 2, 3, 4, 5}

c. A ( (B ( C)

B ( C = {2, 3, 4, 5}
A ( (B ( C) = {5}

d. (A ( B) ( (A ( C)

A ( B = {5}
A ( C = {(}
(A ( B) ( (A ( C) = {5}

e. A’ ( (B’ ( C’)

B’ = {1, 4}
C’ = {1, 3, 5}
B’ ( C’ = {1}
A’ = {2, 3, 4}
A’ ( (B’ ( C’) = {(}

f. (A ( B) – (A ( C)

A ( B = {1, 2, 3, 5}
A ( C = {1, 2, 4, 5}
(A ( B) – (A ( C) = {3}

g. (A ( C)’ (B

A ( C = {(}
(A ( C)’ = {1, 2, 3, 4, 5}
(A ( C)’ ( B = {1, 2, 3, 4, 5}

h. A – (B’ ( C’)

B’ = {1, 4}
C’ = {1, 3, 5}
B’ ( C’ = {1, 3, 4, 5}
A – (B’ ( C’) = {(}

3. Sea U el conjunto de todos los enteros no negativos y considérense los subconjuntos.

A = {x\x es un entero par, 1 _ x < 6} y B = {x\x es un número primo, 0 < x _ 4} Encontrar:

a. A ( B
b. A ( B
c. A’( B’
d. A – B
e. B – A
f. (A – B) ( (B – A)

Rta:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22……(}
A = {2, 4}
B = {2, 3}

a. A ( B
A ( B = {2, 3, 4}

b. A ( B
A ( B = {2}

c. A’ ( B’

A’ = {1, 3, 4, 5, 6, 7, 8, 9 10……(}
B’ = {1, 4, 5, 6, 7, 8, 9, 10……...(}
A’ ( B’ = {1, 4, 5, 6, 7, 8, 9, 10….(}

d. A – B

A – B = {4}e. B – A

B – A = {3}

f. (A – B) ( (B – A)
A – B = {4}
B – A = {3}
(A – B) ( (B – A) = {3,4}

4. Emplear un diagrama de Venn para dibujar cada uno de los conjuntos siguientes:

a. A ( (B ( C)
b. A ( (B ( C)
c. A’ ( (B’ ( C’)
d. (A ( B) – (A ( C)
e. (A ( C)’ ( B
f. A – (B’ ( C’)

Rta:
a. A ( (B ( C)
[pic]
b. A ( (B ( C)
[pic]
c. A’ ( (B’ (C’)

d. (A ( B) – (A ( C)
[pic]

e. (A ( C)’ ( B
[pic]

f. A – (B’ ( C’)
[pic]

6. Sean U = {x/x es un dígito}, A = {1, 2, 3, 5}, B = {2, 4, 5}, C = {4, 5, 6, 7}. Hallar:

a. A ( B
b. A ( C
c. B ( C
d. A ( B
e. A ( C
f. B ( C
g. Ac ( Bc
h. Bc ( (A ( B) c

Rta:

a. A ( B
A ( B = {1, 2, 3, 4, 5}

b. A ( C
A ( C = {1, 2, 3, 4, 5, 6, 7}

c.B ( C
B ( C = {2, 4, 5, 6, 7}

d. A ( B
A ( B = {2, 5}

e. A ( C
A ( C = {5}

f. B ( C
B ( C = {4, 5}

g. Ac ( Bc
Ac = {4, 6, 7, 8, 9}
Bc = {1, 3, 6, 7, 8, 9}
Ac ( Bc = {6, 7, 8, 9}

h. Bc ( (A ( B) c
(A ( B) c = {6, 7, 8, 9}
Bc = {1, 3, 6, 7, 8, 9}
Bc ( (A ( B) c = {6, 7, 8, 9}

ESPACIOS MUESTRALES

7. Clasificar los experimentos en determinísticos y...