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STAT 230
Test 1
May 17, 2006
3:30 – 4:10 pm
1. STAT 230 has three sections in the Spring 2006. Three students (David, Peter and Jon)
registered for the course, and each of them chose a section at random. Find the probabilities
of the following events.
[2] (a) A = “The three students are all in the same section”
P
(
A
) = 3
/
3
3
= 1
/
9.
[2] (b) B = “The three students are all in diﬀerent sections”
P
(
B
) = 3!
/
3
3
= 2
/
9.
[2] (c) C = “None of them is in Section 2”
P
(
C
) = 2
3
/
3
3
= 8
/
27.
[2] (d) D = “At least one of them is in Section 2”
P
(
D
) = 1

P
(
C
) = 19
/
27.
[2] (e) E = “Peter is not in Section 1 and Jon is not in Section 2”
P
(
E
) = (2
×
2
×
3)
/
3
3
= 4
/
9
2. A student club consists of 10 students majored in statistics (ST) and 12 majored in computer
science (CS). Six ST students and ﬁve CS students are female. Suppose
four
club members
are randomly selected (without replacement) to form a
task team
. Let
A = “Exactly two of the team members are CS students”
B = “Exactly two of the team members are female”
[2] (a) Show that
P
(
A
) = 0
.
406 and
P
(
B
) = 0
.
414.
P
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 Fall '06
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