Suppose 97% of the population are law abiding citizens, and the remaining citizens break the law....
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Suppose 97% of the population are law abiding citizens, and the remaining citizens break the law. If an innocent person is arrested, they have a 10% chance of confessing, whereas a guilty person confesses 45% of the time. What is the probability that a person who confessed to a crime is guilty?
Homework Answers
P(guilty| confessed) = P(guilty and confessed)/P(confessed)
P(guilty and confessed) = 0.03*0.45 = 0.0135
P(confessed) = (0.97*0.1)+(0.03*0.45) = 0.097+0.0135 = 0.1105
P(guilty| confessed) = P(guilty and confessed)/P(confessed) = 0.0135/0.1105 = 0.1222
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