a) Suppose you have three coins in a bag: the first coin is fair, wit! ility of HEAD (H) equals to that of TAIL (T), i.e., P(X = H\M1) = P(X = T|M1). is a binary random variable representing HEAD or TAIL. The second is a loaded co (X = H|M2) = 0.8. The third is also a loaded coin with P(X = H\M3) = 0.2. Your kes a coin out of the bag at random and flips it. When it lands, you observe that the e coin facing up is HEAD. What is the probabilities that this is the first, second an in? Hint: You may assume the three coins are equal likely to be selected from the ba M1) = P(M2) = P(M3) = }, and you need to calculate P(M1|X = H), P(M2|X = MalX = H)

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