TP%233b_f08 - CE 3102 Fall 2008 Thought Problem 3b...

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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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CE 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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TP%233b_f08 - CE 3102 Fall 2008 Thought Problem 3b...

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