Math3C HW#2
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Exercise 1
Page805 Ex5
Solution:
A
[
B
=
f
1
;
2
;
3
;
5
g
;
A
\
B
=
f
1
;
3
g
:
°
Exercise 2
Page805 Ex6
Solution:
A
c
=
f
2
;
4
;
6
g
;
(
A
c
)
c
=
f
1
;
3
;
5
g
=
A:
°
Exercise 3
Page805 Ex8
Solution:
Since
A
\
B
=
f
1
;
3
g
;
A and B are not disjoint.
°
Exercise 4
Page805 Ex12
Solution:
Since
A
[
B
= °
)
P
(
A
[
B
) = 1
:
°
Exercise 5
Page805 Ex13
Solution:
P
(
A
c
\
B
c
) =
P
((
A
[
B
)
c
) = 0
:
2
)
P
(
A
[
B
) = 1
°
P
((
A
[
B
)
c
) = 0
:
8
Since
P
(
A
[
B
) =
P
(
A
) +
P
(
B
)
°
P
(
A
\
B
)
)
P
(
B
) =
P
(
A
[
B
)
°
P
(
A
) +
P
(
A
\
B
) = 0
:
8
°
0
:
4 + 0
:
1 = 0
:
5
:
°
Exercise 6
Page805 Ex14
Solution:
Since
P
(
A
[
B
) =
P
(
A
) +
P
(
B
)
°
P
(
A
\
B
)
P
(
A
\
B
) =
P
(
A
) +
P
(
B
)
°
P
(
A
[
B
) = 0
:
4 + 0
:
4
°
0
:
7 = 0
:
1
P
(
A
c
\
B
c
) =
P
((
A
[
B
)
c
) = 1
°
P
(
A
[
B
) = 1
°
0
:
7 = 0
:
3
:
°
Exercise 7
Page805 Ex17
Solution:
° =
f
HH; HT; TH; TT
g
at least one head is
f
HH; HT; TH
g
)
The probability is :
3
4
:
°
Exercise 8
Page805 Ex19
1
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Solution:
° =
°
6
1
± °
6
1
±
= 36
only the °rst one is 4:
1
±
5 = 5
only the second one is 4:
1
±
5 = 5
both two are 4:
1
±
1 = 1
The probability for at least one is 4:
5+5+1
36
=
11
36
:
°
Exercise 9
Page805 Ex21
Solution:
° =
°
6
1
± °
6
1
±
= 36
First way:
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 Spring '07
 SCHONMANN
 Math

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