Reference no: EM132401837

Consider the following simplified view of a jury weighing evidence (treat the jury as a single decision maker). A defendant in a court case is accused of committing a crime. Assume there is potentially one piece of relevant evidence, which is denoted by x. If the defendant is guilty, x is realized with probability pG. If the defendant is innocent, x is realized with probability pI . Assume that if the evidence is realized, the jury automatically observes it. Assume that the jury's prior probability that the defendant is guilty is 1 2 . That is, before observing whether the evidence is realized, the jury assigns a prior probability of 1 2 to the defendant being guilty. Assume that, given the evidence realization (x exists or doesn't), the jury forms an updated belief about the defendant's guilt using Bayes' rule. Suppose pG = 3 4 and pI = 1 8 . Is the realization of evidence x favorable to the defendant? That is, would the defendant prefer that x be realized or not realized? Explain.