EE 351K Probability and Random Processes
FALL 2010
Instructor: Haris Vikalo
[email protected]
Homework 3 Solutions
Problem 1
There are three dice in a bag. One has one red face, another has two red faces, and the
third has three red faces. One of the dice is drawn at random from the bag, each die having an equal chance
of being drawn. The selected die is repeatedly rolled.
1. What is the probability that red comes up on the first roll?
2. Given that red comes up on the first roll, what is the conditional probability that red comes up on the
second roll?
3. Given that red comes up on the first three rolls, what is the conditional probability that the selected
die has red on three faces?
Solution:
Let
E
i
be the event that the die with
i
red faces is drawn from the bag, for
i
= 1
,
2
,
or 3. Let
R
j
denote the event that red comes up on the
j
th role of the die.
1.
P
(
R
1
)
=
P
(
R
1

E
1
)
P
(
E
1
) +
P
(
R
1

E
2
)
P
(
E
2
) +
P
(
R
1

E
3
)
P
(
E
3
)
=
1
6
1
3
+
2
6
1
3
+
3
6
1
3
=
1
3
2. We need to find
P
(
R
2

R
1
)
. First,
P
(
R
1
R
2
)
=
P
(
R
1
R
2

E
1
)
P
(
E
1
) +
P
(
R
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 Spring '10
 Vikalo
 Probability theory, Fischer, R1 R2 R3

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