Chapter 1 Homework; FALL 2011
1. Consider the following CM: A 10sided die
is tossed, with faces marked 1, 2, .
.., 10.
The outcome is the number on the face that
lands up.
(a) Determine the sample space.
(b) List the elements of the following
event:
A
=
the outcome is an odd
number.
(c) List the elements of the following
event:
B
=
the outcome is an even
number larger than 6.
(d) Describe the following event in
words:
C
=
{
7
,
8
,
9
,
10
}
.
2. Refer to the previous exercise. Assume the
ELC. Calculate the probability of each of
the events,
A
,
B
and
C
.
3. A CM has a sample space that consists of
Fve outcomes: 1, 2, 3, 4 and 5. ±or each of
the following assignments, decide whether
it is a mathematically valid way to assign
probabilities for this situation. If not, ex
plain why not.
(a)
P
(1) = 0
.
30
,P
(2) = 0
.
15
(3) =
0
.
25
(4) = 0
.
20
(5) = 0
.
10
.
(b)
P
(1) = 0
.
30
(2) = 0
.
15
(3) =
0
.
20
(4) = 0
.
20
(5) = 0
.
10
.
(c)
P
(1) = 0
.
30
(2) = 0
.
15
(3) =
0
.
25
(4) = 0
.
20
(5) = 0
.
20
.
(d)
P
(1) = 0
.
30
(2) = 0
.
15
(3) =
0
.
25
(4) = 0
.
40
(5) =

0
.
10
.
4. Refer to the previous exercise. Use assign
ment (a) to calculate the probability of each
of the following events.
(a)
A
=
{
1
,
3
,
5
}
.
(b)
B
=
{
2
,
4
}
.
(c)
C
=
{
4
}
.
(d)
D
=
{
3
,
4
,
5
}
.
(e)
E
=
{
1
,
3
}
.
5. Refer to the previous exercise.
(a) Verify that:
P
(
B
or
D
)
±
=
P
(
B
)+
P
(
D
)
.
(b) Verify that Rule 6 is true for events
B
and
D
.
(c) Given that
P
(
B
)=0
.
15 + 0
.
20 =
0
.
35
,e
x
p
l
a
i
nw
h
yy
o
uk
n
o
wt
h
a
t
P
(
A
.
65
without adding the
probabilities of outcomes 1, 3 and 5.
(d) Of the Fve events listed in Exercise 4,
Fnd all pairs that illustrate Rule 5.
6. You are given the following information:
the events
A
and
B
are disjoint;
P
(
A
)=
0
.
30
;and
P
(
B
.
55
.Ca
lcu
la
tethefo
l

lowing probabilities.
(a)
P
(
A
or
B
)
.
(b)
P
(
A
c
)
.
(c)
P
(
B
c
)
.
7. You are given the following information:
P
(
A
.
65
;
P
(
B
.
45
;
P
(
AB
0
.
30
te
P
(
A
or
B
)
.
1