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case, you would like to get a sense of how likely it is that a given defendant was wrongfully convicted at trial. You know that trial juries are not perfect. They only convict guilty defendants 90% of the time, and wrongly convict innocent defendants 10% of the time. You also assess that 75% of the defendants who are brought to trial are actually guilty of their crimes. Using Bayes' rule, determine the probability that a particular defendant is really innocent, given that he or she was convicted by a jury

case, you would like to get a sense of how likely it is that a given defendant was wrongfully convicted at trial. You know that trial juries are not perfect. They only convict guilty defendants 90% of the time, and wrongly convict innocent defendants 10% of the time. You also assess that 75% of the defendants who are brought to trial are actually guilty of their crimes. Using Bayes' rule, determine the probability that a particular defendant is really innocent, given that he or she was convicted by a jury

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Problem Statement:** Suppose you are a judge hearing a criminal appeal. Before looking into the facts of the case, you would like to get a sense of how likely it is that a given defendant was wrongfully convicted at trial. You know that trial juries are not perfect. They only convict guilty defendants 90% of the time, and wrongly convict innocent defendants 10% of the time. You also assess that 75% of the defendants who are brought to trial are actually guilty of their crimes. Using Bayes’ rule, determine the probability that a particular defendant is really innocent, given that he or she was convicted by a jury.
Transcribed Image Text:**Problem Statement:** Suppose you are a judge hearing a criminal appeal. Before looking into the facts of the case, you would like to get a sense of how likely it is that a given defendant was wrongfully convicted at trial. You know that trial juries are not perfect. They only convict guilty defendants 90% of the time, and wrongly convict innocent defendants 10% of the time. You also assess that 75% of the defendants who are brought to trial are actually guilty of their crimes. Using Bayes’ rule, determine the probability that a particular defendant is really innocent, given that he or she was convicted by a jury.
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