Sentences are imposed by: Judges Juries Judges or Juries Neither judges nor juries
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1. (15) Both parts are independent. (a) A person, who is tried by a 3-judge panel, is declared guilty if at least 2 judges cast votes of guilty. When the defendant is, in fact, guilty, each judge will independently vote guilty with probability .7; whereas when the defendant is, in fact, innocent, this probability drops to .2. Suppose 70 percent of defendants are guilty. For i = 1, 2, 3, let Ji be the event that Judge i votes guilty. (i) Determine the probability that Judge 3 votes guilty when Judge 1 and Judge 2 vote guilty. (ii) Determine the probability that the defendant is guilty if he is judged guilty. (There is no need to simplify arithmetic expressions.)
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