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Probability with Applications
Dr. Polly B. He
Practice Midterm 1
You have 50 minutes to complete the exam.
In order to get partial credit, you should show clearly the steps of your work. Leave your
answer in the form of
e

1
,
(
5
3
)
, etc
.
Problem 1 (20 points)
A monkey at a typewriter types each of the 26 letters of the alphabet exactly once, the order
being random.
(a) Deﬁne a suitable sample space.
(b) What is the probability that the word “Hamlet” appears somewhere in the string of
letters?
Problem 2 (25 points)
A person is diagnosed with an uncommon disease. There is a 1% chance of getting it. Use
the letter
D
for the event “the person has the disease” and
T
for “the test says no”. It is
known that the test is imperfect:
P
(
T

D
) = 0
.
98 and
P
(
T
c

D
c
) = 0
.
95. Given that the test
is positive, what is the probability that the person really has the disease?
1
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 Fall '08
 Zahrn

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