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STOR 435
Exam 1
Fall 2009
(1) Assume that events
A
and
B
are independent, events
A
and
C
are independent, and
B
⊂
C
. Moreover,
P
(
A
) = 1
/
3,
P
(
B
) = 1
/
4, and
P
(
C
) = 1
/
2.
(a) Draw a Venn diagram.
(b) Calculate
P
(
A
∩
B
c
∩
C
).
(c) Calculate
P
(
C

A
c
∩
B
c
).
(d) Calculate
P
(
B
or
C

A
).
(2) 8 people (5 women and 3 men) are divided into two diﬀerent groups of equal size.
(a) What is the probability that Group 1 consists of an equal number of men and
women?
(b) Given that Group 1 contains at least 1 woman, what is the conditional probability
that Group 2 contains more women than men?
(3) The curriculum in a certain high school is designed according to 3 diﬀerent career paths,
denoted by
C
1
,
C
2
and
C
3
. The proportions of students in these 3 paths are 50%, 30%
and 20% respectively. Suppose 20% of the students in
C
1
, 15% of the students in
C
2
and
10% of the students in
C
3
have their GPA “3.5 or higher”.
(a) Construct a tree diagram.
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 Fall '08
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