Question 1 (Bayes' rule) You have four coins in the bag: Coin 1 (C1) is a fair coin that comes up heads with probability 0.5 Coin 2 (C2) is a biased coin that comes up heads with probability 0.2 Coin 3 (C3) is a biased coin that comes up heads with probability 0.4 Coin 4 (C4) is a biased coin that comes up heads with probability 0.8 Suppose you pick one of the coins uniformly at random and flip it four times. If you observe the sequence HTHT (where H indicates heads and T indicates for tails), what is the probability that you chose Coin 3? Explain your answer. P(C3 | HTHT) =