36. Consider all courtroom trials with a single de-fendant who is charged with a felony. Supposethat you are given the following probabilities forthis situation.Seventy-five percent of the defendants are, infact, 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 notguilty, there is a 40 percent chance the jury willconvict the person.For simplicity, assume that the only optionsavailable to the jury are: to convict or to releasethe defendant.(a) What proportion of the defendants will beconvicted by the jury?38(b) Given that a defendant is convicted, whatis the probability the person is, in fact,guilty?(c) What is the probability that the jury willmake 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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Answered: (a) What proportion of the defendants…

A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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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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(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?