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CE 3102
Fall 2008
Thought Problem 3b
Prosecutor’s Fallacy?
A crime has been committed, and the perpetrator left DNA evidence at the scene. A
suspect has been identified, and a sample of the suspect’s DNA matches the DNA left at
the crime scene. The testing laboratory states that the chance of a false match is only 1 in
one million. A prosecutor then argues that the probability that the suspect is innocent is
only 1 in one million. Is this conclusion justified? Why or why not?
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View Full DocumentCE 3102
Fall 2008
Thought Problem 3b
Instructor’s Partial Solution
First, let’s translate this problem into mathematical notation. Let M denote the event “the
DNA samples match” and G denote the event “the suspect is guilty.” According to the
testing lab
6
10
)

(
−
=
G
M
P
while the prosecutor is claiming that
6
10
)

(
−
=
M
G
P
These two conditional probabilities are related via Bayes’ theorem
)
(
)

(
)
(
)

(
)
(
)

(
)

(
G
P
G
M
P
G
P
G
M
P
G
P
G
M
P
M
G
P
+
=
and inspection of this equation suggests
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 Spring '11

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