1. (5 pt) We have the more general form of the product rule below. P(x1 , . . ., In | y1 . . . ym) = P(x1 . . . In, y1 , . . . , ym) P ( y1 , . .. . ym Using this, prove the conditional form of Bayes' law P(xly, z) = P(yx, z) P(x z) P(ylz) 2. There are two types of coins: real coins and fake (counterfeit) coins. Real coins flips heads with probability p, and tails with probability 1 - p. Counterfeit coins flip heads with probability q, and tails with probability 1 - q. The coins otherwise look totally identical, with no other distinguishing features. Both p and q are fixed, known constants, with 0