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Unformatted text preview: statement of the problem; the conditional probabilities the other way around were given, , as were the unconditional probabilities of the partitioning sets B 1 and B 2 . The Law of Total Probability and the Multiplicative Law of Probability , together with the definition of conditional probability, allow us to calculate the desired probability in situations like this, and this method is called Bayes Rule . by the definition of conditional probability, so by the Law of Total Probability and the Multiplicative Law of Probability, - 2 - John J Currano, 12/12/2008 . This is what is known as Bayes Rule or Bayes Theorem . Since we have already calculated P ( A ) in part (a), and also calculated the numerator of the fraction in the process of doing that, we see that The following tree, obtained using the texts applet, illustrates these computations. In the tree, B = B 1 , ~ B = = B 2 , and ~ A = ....
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