190
Solutions to Exercises
5.
[BB]
(a)
(b)
(~)
_
15.
M 
64'
(c)
1
+
(~)
+
(~)
_
11.
64

32'
6.
(a)
(d)
(d)
1
1
_
63.
6464'
1
+
G)
1
~=16
(b)
(e)
(~)
+
(~)
+
(~)

1
64

2'
(e)
G)=~
128
128
(i)+G)+G)+G)
_1
128

2"
(c)
1
1
+
(i)
_
15.
~16'
7.
[BB]
(a) There are
(~)
outcomes
in
the sample space. For an outcome to
be
in the event described, we
need to choose three from the six selected numbers and three from the 43 other numbers. The answer
l
'S
m
(~)
~
0 018
(~)
~.
.
1
(c)
1 
(~)
~
1.000.
9.
[BB]
(a)
1~~~~)
=
i;
(b)
1
i
=~;
(c)
1
l~f~~)
=~;
(d)
;1W~?
=
1
5
8;
(e) We will use the formula given
in
part (3)
of
Theorem 7.3.2.
Let
A
be the event "at least one white
ball" and
B
be
"exactly one red ball." We saw in (c) that
P(A)
=
~.
Also
P(B)
=
;Wg?
=
~~.
Since
An
B
is the event described in (d),
P(A
n
B)
=
1
5
8'
The required probability is
P{A
U
B)
=
5
35
5
55
9"
+
72 
18
=
72'
10
()
3(3)
_
1 .
. a
12(12)

16'
(b) 1
1 
15.

16

16'
( ) 1
9(9)
_
7.
C

12(12)

16'
(
d)
2(3)(4)
=
1·
12('12)
6'
(e) Let
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 Summer '10
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 Graph Theory, Probability theory, 1W, 2 2, 5 18

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