Math331, Spring 2008
Instructor: David Anderson
Section 1.1 and 1.2 Hw answers
Homework:
pgs. 9  11, #’s 2, 3, 5, 9, 13, 17(a)
2. The sample space is given by
S
=
{
(
i,j,k
)

i,j,k
∈ {
red,blue
}}
.
3. The sample space is
S
=
{
t
:
t
∈
(0
,
20)
}
. The event that the number is an integer is
E
=
{
1
,
2
,
3
,...,
19
}
.
5.
E
is the event that the sum is odd.
F
is the event that at least one 1 is rolled.
E
∩
F
implies one 1 and one even number (so the sum is odd).
E
c
∩
F
implies one 1 and one odd
number (so the sum is even).
E
c
∩
F
c
implies the sum is even and neither was a 1. Thus,
both even or both in
{
3
,
5
}
.
9.
Let
a
i
b
j
be the event that passenger
a
gets off at hotel
i
and likewise for
b
.
Here
i,j
∈ {
1
,
2
,
3
}
. Then
S
=
{
a
i
b
j
:
i,j
∈ {
1
,
2
,
3
}}
.
Alternatively (there is no unique answer
here)
S
=
{
(
i,j
) :
i,j
∈ {
1
,
2
,
3
}}
, where the first element of (
·
,
·
) represents the number
of the hotel (1,2, or 3) that passenger
A
gets off at and the second element represents the
number of the hotel for passenger
B
.
The event that both get off at the same hotel is
{
(1
,
1)
,
(2
,
2)
,
(3
,
3)
}
.
13.
(a)
E

E
∩
F
=
E
∩
(
E
∩
F
)
c
=
E
∩
(
E
c
∪
F
c
) = (
E
∩
E
c
)
∪
(
E
∩
F
c
) =
E
∩
F
c
. Thus,
(
E

E
∩
F
)
∪
F
= (
E
∩
F
c
)
∪
F
= (
E
∪
F
)
∩
(
F
c
∪
F
) = (
E
∪
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 Spring '08
 Anderson
 Math, Probability

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