Question 255711: A jury has 12 jurors. A vote of at least 10 of 12 for "guilty" is necessary for a defendant to be convicted of a crime. Assume that each juror acts independently of the others and that the probability that any one juror makes the correct decision on a defendant is 0.69. If the defendant is guilty, what is the probability that the jury makes the correct decision?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A jury has 12 jurors. A vote of at least 10 of 12 for "guilty" is necessary for a defendant to be convicted of a crime. Assume that each juror acts independently of the others and that the probability that any one juror makes the correct decision on a defendant is 0.69. If the defendant is guilty, what is the probability that the jury makes the correct decision?
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It's a binomial problem with n=12, p = 0.69, 10 <= x <= 12
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P(10<= x <= 12) = 1 - binomcdf(12,0.69,9) = 0.2296..
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Cheers,
Stan H.
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