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Section 7.3
191
13 [BB] (a)
(~)
G)
= 2.
·
C;)
44
(d) Let
A
be "majority of Americans" and
B
be "exactly four Canadians." From (a) and (b), we know
P( A)
=
~
and
P( B)
=
~~.
Since
A
n
B
=
0,
A
and
B
are mutually exclusive, so the answer is
P(A
U
B)
=
~
+
14
=
~4'
(d) Let
A
be "exactly three Americans" and
B
be "at most three Canadians." From (a) and (c), we
know
P(A)
=
~~
and
P(B)
=
i~~.
The event "three Americans and two Canadians" is
A
n
B,
but this is just
A.
Thus
U
=
~~
+
i~~

~~
=
i~~.
15.
[BB]
(a)
i~
(b)
1~
(c)
i
(d)
1~
(e)
~
16.
(a)
~gg
(b)
2
3
l
o
(c)
lo~
17. Let
A
be "divisible by 3,"
B
be "divisible by 5," and C be "divisible by 7." We want
U
B
U C) 
n
B
n C)
= P(A)
+
+
P(C)

n

n C) 
P(B
n C)
1666
1000
714
333
238
142
2667
=
5000
+
+
5000 
=
5000'
18. (a) Using Exercise 15(a) of Section 6.1, we obtain
1~~~gO
=
~6g~.
L
10,000
J
(b) This means divisible by 3(5)
(7)
(11)
=
1155, so the answer is
1~1~~0
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory, Mutually Exclusive

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