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Solution for HW1
STA113 ISDS
September 5, 2004
§
13.
a.
A
1
∪
A
2
=
{
awarded project 1 or 2
}
P
(
A
1
∪
A
2
) =
P
(
A
1
) +
P
(
A
2
)

P
(
A
1
∩
A
2
)
= 0
.
22 + 0
.
25

0
.
11 = 0
.
36
b.
A
0
1
∩
A
0
2
=
{
awarded neither project 1 nor 2
}
P
(
A
0
1
∩
A
0
2
) =
P
((
A
1
∪
A
2
)
0
) = 1

P
(
A
1
∪
A
2
) = 0
.
64
c.
A
1
∪
A
2
∪
A
3
=
{
awarded at least one project from 1 ,2, and 3
}
P
(
A
1
∪
A
2
∪
A
3
) =
P
(
A
1
) +
P
(
A
2
) +
P
(
A
3
)

P
(
A
1
∩
A
2
)

P
(
A
1
∩
A
3
)

P
(
A
2
∩
A
3
) +
P
(
A
1
∩
A
2
∩
A
3
)
= 0
.
53
d
A
0
1
∩
A
0
2
∩
A
0
3
=
{
awarded none of 1,2,3
}
P
(
A
0
1
∩
A
0
2
∩
A
0
3
) =
P
((
A
1
∪
A
2
∪
A
3
)
0
) = 1

0
.
53 = 0
.
47
1
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View Full Documente.
A
0
1
∩
A
0
2
∩
A
3
=
{
only awarded project 3
}
P
(
A
0
1
∩
A
0
2
∩
A
3
) = 0
.
17
Hint
:
P
(
A
0
1
∩
A
0
2
∩
A
3
) +
P
(
A
0
1
∩
A
0
2
∩
A
0
3
) =
P
(
A
0
1
∩
A
0
2
)
f, (
A
0
1
∩
A
0
2
)
∪
A
3
=
{
awarded project 3, or awarded neither project 1 nor 2
}
P
((
A
0
1
∩
A
0
2
)
∪
A
3
) =
P
(
A
0
1
∩
A
0
2
)+
P
(
A
3
)

P
(
A
0
1
∩
A
0
2
∩
A
3
) = 0
.
75
§
26.
a.
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