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EE 351K Probability and Random Processes
FALL 2010
Instructor: Haris Vikalo
hvikalo@ece.utexas.edu
Homework 1
Due on : Tuesday 09/07/10
Problem 1
We are given that
P
(
A
) = 0
.
55
,
P
(
B
c
) = 0
.
45
, and
P
(
A
∪
B
) = 0
.
85
. Determine
P
(
B
)
and
P
(
A
∩
B
)
.
Problem 2
Let
A
and
B
be two sets.
(a) Show that
(
A
c
∩
B
c
)
c
=
A
∪
B
and
(
A
c
∪
B
c
)
c
=
A
∩
B
.
(b) Consider rolling a sixsided die once. Let
A
be the set of outcomes where an odd number comes
up. Let
B
be the set of outcomes where a
1
or a
2
comes up. Calculate the sets on both sides of the
equalities in part (a), and verify that the equalities hold.
Problem 3
Alice and Bob each choose at random a number between zero and two. We assume a uniform
probability law under which the probability of an event is proportional to its area. Consider the following
events:
A: The magnitude of the difference of the two numbers is greater than
1
/
3
.
B: At least one of the numbers is greater than
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 Spring '10
 Vikalo

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