Statistical Methods (STAT 511)
Midterm #1, Spring 2011
8:0010:00pm, LWSN B155
Thursday, February 24, 2011
There are totally 27 points in the exam. The students with score higher than or equal to 25
points will receive 25 points. Please write down your name, student ID number, and mark your
devision below.
NAME:
ID:
1
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1. (6 points). A bag has 30 blue balls, 25 red balls, and 20 yellow balls. Randomly choose 6 of them.
(a) (2 point). Compute the probability of the event that there are exactly 2 balls for each color.
P
(
B
= 2
, R
= 2
, Y
= 2) =
(
30
2
)(
25
2
)(
20
2
)
(
75
6
)
= 0
.
1231
.
(b) (2 points). Compute the probability of the event that there are no yellow balls.
P
(
Y
= 0) =
(
55
6
)
(
75
6
)
= 0
.
1440
.
(c) (2 points). Compute the probability of the event that there are at most two yellow balls.
P
(
Y
≤
2) =
P
(
Y
= 0) +
P
(
Y
= 1) +
P
(
Y
= 2)
=
(
55
6
)
(
75
6
)
+
(
55
5
)(
20
1
)
(
75
6
)
+
(
55
4
)(
20
2
)
(
75
6
)
=0
.
1440 + 0
.
3455 + 0
.
3218
=0
.
8113
.
2. (6 points).
Suppose
A
,
B
and
C
are events, and
P
(
A
) = 0
.
6,
P
(
B

A
) = 0
.
3,
P
(
B

A
0
) = 0
.
4,
P
(
C

A
∩
B
) = 0
.
25,
P
(
C

A
0
∩
B
) = 0
.
35,
P
(
C

A
∩
B
0
) = 0
.
7,
P
(
C

A
0
∩
B
0
) = 0
.
55.
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