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(a) What proportion of the defendants will be convicted by the jury? 38 (b) Given that a defendant is convicted, what is the probability the person is, in fact, guilty? (c) What is the probability that the jury will make a correct decision?

(a) What proportion of the defendants will be convicted by the jury? 38 (b) Given that a defendant is convicted, what is the probability the person is, in fact, guilty? (c) What is the probability that the jury will make a correct decision?

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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36. Consider all courtroom trials with a single de- fendant who is charged with a felony. Suppose that you are given the following probabilities for this situation. Seventy-five percent of the defendants are, in fact, guilty. Given that the defendant is guilty, there is a 70 percent chance the jury will con- vict the person. Given that the defendant is not guilty, there is a 40 percent chance the jury will convict the person. For simplicity, assume that the only options available to the jury are: to convict or to release the defendant. (a) What proportion of the defendants will be convicted by the jury? 38 (b) Given that a defendant is convicted, what is the probability the person is, in fact, guilty? (c) What is the probability that the jury will make a correct decision? (d) Given that the jury makes an incorrect de- cision, what is the probability that the de- cision is to release a guilty person?
Transcribed Image Text:36. Consider all courtroom trials with a single de- fendant who is charged with a felony. Suppose that you are given the following probabilities for this situation. Seventy-five percent of the defendants are, in fact, guilty. Given that the defendant is guilty, there is a 70 percent chance the jury will con- vict the person. Given that the defendant is not guilty, there is a 40 percent chance the jury will convict the person. For simplicity, assume that the only options available to the jury are: to convict or to release the defendant. (a) What proportion of the defendants will be convicted by the jury? 38 (b) Given that a defendant is convicted, what is the probability the person is, in fact, guilty? (c) What is the probability that the jury will make a correct decision? (d) Given that the jury makes an incorrect de- cision, what is the probability that the de- cision is to release a guilty person?
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