4. The prosecutor\'s fallacy: You are on the jury for a murder trial, and have t

Question

4. The prosecutor's fallacy: You are on the jury for a murder trial, and have to decide whether the accused person is guilty or innocent. The sole piece of evidence presented against the accused is a DNA match. There is good scientific evidence indicating that the probability of a DNA match for an innocent person is T, and that the probability of a DNA match for a guilty person is . A DNA match has been established for the accused person, and the prosecutor claims that this is definitive evidence indicating the guilt of the accused. There are 10,000 residents in the city and before seeing the evidence your best judgment is that it is equally likely that any one of these residents committed the crime. So summarizing: Pl match!guilty)-99, P(match innocent) = TR5-PGuilty) = TO (a) What is P(guilty match)? (b) What is P(innocent match)? 1,000 100 1,000

Explanation / Answer

a) here P(match)=P(guility)*P(match|guilty)+P(innocent)*P(match|innocent)

=(1/10000)*(99/100)+(1-1/10000)*(1/1000)=0.0010989

therefore P(guilty|match)=P(guility)*P(match|guilty)/P(match)=(1/10000)*(99/100)/0.0010989 =0.0901

b)P(innocent|match) =P(innocent)*P(match|innocent)/P(match)=(1-1/10000)*(1/1000)/0.0010989 =0.9099

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