The probability that a three-person jury will make a correct decision is given by the function below, where 0

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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The probability that a three-person jury will make a correct decision is given by the function below, where 0<x< 1 is the probability the person is guilty of the crime, r is the probability that a given
jury member will vote "guilty" when the defendant is indeed guilty of the crime, and s is the probability that a given jury member will vote "innocent" when the defendent is indeed innocent.
Complete parts a through c.
P(a,r,s) = a[3r²(1-r) +r³]+(1-a)[3s²(1-s)+s³]
a. Calculate P(0.9,0.6,0.8) and P(0.1,0.8,0.4) and interpret your answers.
P(0.9,0.6,0.8)=
(Do not round until the final answer. Then round to three decimal places as needed.)
Transcribed Image Text:K The probability that a three-person jury will make a correct decision is given by the function below, where 0<x< 1 is the probability the person is guilty of the crime, r is the probability that a given jury member will vote "guilty" when the defendant is indeed guilty of the crime, and s is the probability that a given jury member will vote "innocent" when the defendent is indeed innocent. Complete parts a through c. P(a,r,s) = a[3r²(1-r) +r³]+(1-a)[3s²(1-s)+s³] a. Calculate P(0.9,0.6,0.8) and P(0.1,0.8,0.4) and interpret your answers. P(0.9,0.6,0.8)= (Do not round until the final answer. Then round to three decimal places as needed.)
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