This preview shows pages 1–2. Sign up to view the full content.
Solutions to Homework 2, ISyE 2027 Fall 2006
Problem 1
(a) Let
A
=
{
H, T
}
(where
H
denotes heads and
T
represents tails), and let
B
=
{
1
,
2
,
3
,
4
,
5
,
6
}
. A reasonable sample space
S
is
A
×
B
, where
A
×
B
:=
{
(
i, j
) :
i
∈
A, j
∈
B
}
.
(b) There are (2)(6) = 12 outcomes in
S
.
(c) If the die and coin are fair, then the outcomes are equally likely.
Problem 2
(a)
P
(
A
) = 1

P
(
A
) = 1

.
4 =
.
6.
(b)
P
(
A
∪
B
) =
P
(
A
) +
P
(
B
)

P
(
A
∩
B
) =
.
4 +
.
3

.
1 =
.
6.
(c) DeMorgan’s law tells us that
A
∪
B
=
A
∩
B
, so
P
(
A
∩
B
) =
P
(
A
∪
B
) = 1

P
(
A
∪
B
) = 1

.
6 =
.
4
.
(d)
P
(
A
∪
B
) =
P
(
A
) +
P
(
B
)

P
(
A
∩
B
) =
.
6 +
.
7

.
4 =
.
9.
(e)
A
and
B
are not disjoint, since
P
(
A
∩
B
) =
.
1
>
0. Recall that two sets are
disjoint if
A
∩
B
=
∅
. We also know that
P
(
∅
) = 0, which excludes the possibility
of
A
and
B
being disjoint.
Problem 3
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Zahrn

Click to edit the document details