DS 212 Business Statistics
Soorapanth
Homework #4 Solutions
4.2
X = {1, 3, 5, 7, 8, 9}, Y = {2, 4, 7, 9}, and Z = {1, 2, 3, 4, 7,}
a)
X
∪
Z =
{1, 2, 3, 4, 5, 7, 8, 9}
b)
X
∩
Y =
{7, 9}
c)
X
∩
Z =
{1, 3, 7}
d)
X
∪
Y
∪
Z =
{1, 2, 3, 4, 5, 7, 8, 9}
e)
X
∩
Y
∩
Z =
{7}
f)
(X
∪
Y)
∩
Z = {1, 2, 3, 4, 5, 7, 8, 9}
∩
{1, 2, 3, 4, 7}
=
{1, 2, 3, 4, 7}
g)
(Y
∩
Z)
∪
(X
∩
Y) = {2, 4, 7}
∪
{7, 9} =
{2, 4, 7, 9}
h)
X or Y = X
∪
Y =
{1, 2, 3, 4, 5, 7, 8, 9}
i)
Y and Z = Y
∩
Z =
{2, 4, 7}
4.3
If A = {2, 6, 12, 24} and the population is the positive even numbers
through 30,
A’ =
{4, 8, 10, 14, 16, 18, 20, 22, 26, 28, 30}
4.6
10
7
= 10,000,000 different numbers
4.7
20
C
6
=
!
14
!
6
!
20
=
38,760
It is assumed here that 6 different (without replacement) employees are to
be selected.
4.8
P
(A) = .10,
P
(B) = .12,
P
(C) = .21,
P
(A
∩
C) = .05
P
(B
∩
C) = .03
a)
P
(A
∪
C) =
P
(A) +
P
(C) -
P
(A
∩
C) = .10 + .21 - .05 =
.26
b)
P
(B
∪
C) =
P
(B) +
P
(C) -
P
(B
∩
C) = .12 + .21 - .03 =
.30
c) If A, B mutually exclusive,
P
(A
∪
B) =
P
(A) +
P
(B) = .10 + .12 =
.22
4.9
D
E
F
A
5
8
12
25
B
10
6
4
20
C
8
2
5
15
23
16
21
60
1