Question: An individual tried by a three-judge panel is declared guilty if at least two judges cast votes of guilty. Suppose that when the defendant is,

An individual tried by a three-judge panel is declared guilty if at least two judges cast votes of guilty. Suppose that when the defendant is, in fact, guilty, each judge will independently vote guilty with probability 0.7 but, if the defendant is, in fact, innocent, each judge will independently vote guilty with probability 0.2. Assume that 70% of the defendants are actually guilty. If a defendant is judged guilty by the panel of judges, what is the probability he is actually innocent?

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