10
Chapter 2
Chapter 2
Problems
1.
(a)
S
= {(
r
,
r
), (
r
,
g
), (
r
,
b
), (
g
,
r
), (
g
,
g
), (
g
,
b
), (
b
,
r
),
b
,
g
), (
b
,
b
)}
(b)
S
= {(
r
,
g
), (
r
,
b
), (
g
,
r
), (
g
,
b
), (
b
,
r
), (
b
,
g
)}
2.
S
= {(
n
,
x
1
, …,
x
n
−
1
),
n
≥
1,
x
i
≠
6,
i
= 1, …,
n
−
1}, with the interpretation that the outcome is
(
n
,
x
1
, …,
x
n
−
1
) if the first 6 appears on roll
n
, and
x
i
appears on roll,
i
,
i
= 1, …,
n
−
1.
The
event
c
n
n
E
)
(
1
∞
=
∪
is the event that 6 never appears.
3.
EF
= {(1, 2), (1, 4), (1, 6), (2, 1), (4, 1), (6, 1)}.
E
∪
F
occurs if the sum is odd or if at least one of the dice lands on 1.
FG
= {(1, 4), (4, 1)}.
EF
c
is the event that neither of the dice lands on 1 and the sum is odd.
EFG
=
FG
.
4.
A
= {1,0001,0000001, …}
B
= {01, 00001, 00000001, …}
(
A
∪
B
)
c
= {00000 …, 001, 000001, …}
5.
(a) 2
5
= 32
(b)
W
= {(1, 1, 1, 1, 1), (1, 1, 1, 1, 0), (1, 1, 1, 0, 1), (1, 1, 0, 1, 1), (1, 1, 1, 0, 0), (1, 1, 0, 1, 0)
(1, 1, 0, 0, 1), (1, 1, 0, 0, 0), (1, 0, 1, 1, 1), (0, 1, 1, 1, 1), (1, 0, 1, 1, 0), (0, 1, 1, 1, 0), (0, 0, 1, 1, 1)
(0, 0, 1, 1, 0), (1, 0, 1, 0, 1)}
(c) 8
(d)
AW
= {(1, 1, 1, 0, 0), (1, 1, 0, 0, 0)}
6.
(a)
S
= {(1,
g
), (0,
g
), (1,
f
), (0,
f
), (1,
s
), (0,
s
)}
(b)
A
= {(1,
s
), (0,
s
)}
(c)
B
= {(0,
g
), (0,
f
), (0,
s
)}
(d) {(1,
s
), (0,
s
), (1,
g
), (1,
f
)}
7.
(a) 6
15
(b) 6
15
−
3
15
(c) 4
15
8.
(a) .8
(b) .3
(c) 0
9.
Choose a customer at random.
Let A denote the event that this customer carries an American
Express card and V the event that he or she carries a VISA card.
P
(
A
∪
V
) =
P
(
A
) +
P
(
V
)
−
P
(
AV
) = .24 + .61
−
.11 = .74.
Therefore, 74 percent of the establishment’s customers carry at least one of the two types of
credit cards that it accepts.