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Consider a jury trial in which it takes 12 of 16 jurors to convict the defendant; that is, in order for the defendant to be

Consider a jury trial in which it takes 12 of 16 jurors to convict the defendant; that is, in order for the defendant to be convicted, at least 12 of the jurors must vote him guilty. If we assume that jurors act independently and that, whether or not the defendant is guilty, each makes the right decision with probability 3/4 , what is the probability that the jury renders a correct decision given that the defendant is guilty with probability1/2

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