University of Illinois
Spring 2010
ECE 313:
Problem Set 6
Due:
Wednesday, March 3rd at 4 p.m.
Reading:
Ross, Chapter 3; Lecture Notes 1418.
Noncredit Exercises:
DO NOT turn these in.
Chapter 3:
Problems 80,84 and 86;
Theoretical Exercises 8,16 and 21.
This Problem Set contains seven problems.
1.
[Conditional Probability]
Die
A
has four red and two white faces, whereas die
B
has two red and four white
faces. A fair coin is flipped once. If it falls heads, the game continues by throwing die
A
alone. If it falls tails, die
B
is to be used.
(a) Show that the probability of red at any throw is 1
/
2.
(b) If the first throw resulted in red, what is the probability of red in the third throw?
(c) If red turns up in the first
n
throws, what is the probability that die
A
is being
used?
2.
[Conditional Probability and Poisson Random Variables]
Each customer who enters Laura’s clothing store will purchase a suit with probability
p
. If the number of customers entering the store is Poisson distributed with mean
λ
,
what is the probability that Laura does not sell any suits? What is the probability of
her selling
k
suits?
3.
[Law of total probability]
Alice and Bob play the following game. First, Alice rolls a fair die and then Bob rolls
the fair die. If Bob rolls a number at least as large as Alice’s number, he wins the
game. But if Bob rolled a number smaller than Alice’s number, then Alice rolls the
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 Spring '08
 Milenkovic,O
 Probability, Probability theory, Alice

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