STAT 550 HW #3 Solution
1.51
{( , ), ,
1
6}
{(3,4),(4,3)}
{
7}
{(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)}
2
6
1
2
(
)
,
(
)
,
(
)
36
36
6
36
(
)
2 / 36
1
(

)
(
)
1/ 6
3
sample space S
i j
i j
A
B
the sum of face is
P A
P B
P A
B
P A
B
P A B
P B
=
=
=
=
=
=
=
=
=
=
=
=
K
I
I
1.54
(a)
5
5
4
1
1
1
5
5
4
3
⎛
⎞⎛
⎞⎛
⎞
⎜
⎟⎜
⎟⎜
⎟
⎝
⎠⎝
⎠⎝
⎠
+
+
⎛
⎞
⎜
⎟
⎝
⎠
(b) Let A, B, C be events that there is a person selected in Democrats, Republicans and
Independents respectively:
1
1
1
5
5
4
1
1
1
14
13
12
(
)
(
)
(

)
(

)
P A B C
P A P B
A P C
A B
C
C
C
C
C
C
⋅
⋅
=
⋅
=
⋅
⋅
1.55
(a)
0.15
1
(
4

)
0.6
4
P more than
hours student is in a tech area
=
=
(b)
0.15
3
(

4
)
0.15
0.05
4
P student is in a tech area more than
hours
=
=
+
(c)
0.20
0.15
7
(

4
)
0.25
0.55
16
P student is in a nontech area less than or equal to
hours
+
=
=
+
1.56
Let E be an event that red marble is selected in BOX I; A be an event that the marble is red in
BOX II. Then
2
2
4
(
)
,
(
)
,
(

)
,
(

)
4
4
6
C
C
P E
P E
P A E
P A E
=
=
=
3
6
=
By the total probability, we have
2
4
2
3
7
(
)
(
)
(

)
(
)
(

)
4
6
4
6
12
C
C
P A
P E P A E
P E
P A E
=
+
=
×
+
×
=
1.58
Let A be the event that a student will graduate, E be the event that a student will study
1
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