IE 111 Fall Semester 2007
Homework #1
Due Wednesday
9/5/07
Question 1.
Consider the Venn diagram at right with
events A, B, C, and D as shown when
you answer questions a) through e).
a)
Give a set representation of the shaded
region.
Indicate the most appropriate answer for each of
the following questions (where NMI means “need
more information”).
b)
T
F
NMI
(A
∩
B
′
)
∩
D
and
(A
∩
D)
∩
C
′
are mutually exclusive.
c)
T
F
NMI
B and C are independent
d)
T
F
NMI
P(AB) ≥ P(BA)
e)
T
F
NMI
P(B) ≤ P(D)
Question 2.
A Lehigh student is selected at random and the student’s class x (Frosh, Soph, junior,
Senior, or Grad), sex y (Male, Female), and living arrangement z (dorm, frat, sorority,
offcampus) are observed.
Note the following Lehigh rules:
 Frosh must live in dorms.
 Frats are limited to under grad men, sororities to under grad women.
 Grad students must live off campus.
a)
Describe the sample space of this experiment by listing its elements in the form
(x,y,z).
b)
Use a tree diagram to describe the sample space in question 1.
Question 3.
An experiment consists of throwing a pair of dice, one maize (yellow), and the other blue.
If x is the number showing on the maize die, and y is the number showing on the blue
die, then an outcome can be represented as (x,y).
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 Spring '07
 Storer

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