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EE 351K Probability and Random Processes
FALL 2010
Instructor: Haris Vikalo
hvikalo@ece.utexas.edu
Homework 2
Due on : Tuesday 09/14/10
Problem 1
Bob, Carol, Ted and Alice take turns (in that order) tossing a coin with probability of tossing
a Head,
P
(
H
) =
p
, where
0
< p <
1
. The ﬁrst one to toss a Head wins the game. Calculate
P
(
B
)
,
P
(
C
)
,
P
(
T
)
, and
P
(
A
)
, the
win probabilities
for Bob, Carol, Ted and Alice, respectively. Also show that
•
P
(
B
)
> P
(
C
)
> P
(
T
)
> P
(
A
)
.
•
P
(
B
) +
P
(
C
) +
P
(
T
) +
P
(
A
) = 1
.
Problem 2
A new test has been developed to determine whether a given student is overstressed. This
test is 90% accurate if the student is not overstressed, but only 80% accurate if the student is overstressed. It
is known that 60% of all students are overstressed. Given that a particular student tests negative for stress,
what is the probability that the test result is correct?
Problem 3
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 Spring '10
 Vikalo

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