Hang Seng Management College
Department of Mathematics and Statistics
STA 101 Introduction to Statistics
Test 2 (20092010) (Total mark: 45)
1.
Suppose P(A) = 0.2, P(B) = 0.6, and
2
.
0
)

(
=
B
A
P
.
(a)
Find
)
(
B
A
P
∩
.
(b)
Draw a Venn diagram to illustrate P(A), P(B) and
)
(
B
A
P
∩
.
(c)
Find
)
(
B
A
P
∪
.
(d)
Find
)

(
A
B
P
.
(e)
Are A and B mutually exclusive? Explain using probabilities.
(12 marks)
2.
A box contains four red and three blue poker chips. What is the probability when
three are selected randomly that exactly two will be red if we select each chip
(a)
with replacement?
(b)
without replacement?
(5 marks)
3.
A statistics professor classifies his students according to their grade point
average (GPA) and their gender. The accompanying table gives the proportion
of students falling into the various categories. One student is selected at
random.
GPA
Gender
Under 2.0
2.0 – 3.0
Over 3.0
Male
0.05
0.25
0.10
Female
0.10
0.30
0.20
(a)
What is the probability that the GPA is over 3.0?
(b)
If the GPA of the student selected is over 3.0, what is the probability
that the student is male?
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 Fall '10
 Ying
 Statistics, Probability, Probability theory, Randomness, 1minute period, Seng Management College Department of Mathematics

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