3] Suppose there are four unmarked boxes, A, B, C, D. Box A contains three gold coins; B contains two gold coins and one silver coin; C contains one gold coin and two silver coins: and D contains three silver coins. Suppose you randomly select one ofthe boxes and pull out a single coin and it is gold. So event E is you chose one of the gold coins. outcome A61 A62 A63 361 362 BS CG C51 C82 D81 DSZ D53 1 1 1 1 1 1 1 1 1 1 1 1 E E E E E E E E E E E E EventE / / '/ / / / conditional on E prior a [10 points] Compute the conditional probabilities of all 12 coins, conditional on E and fill in the bottom row of the above. b] Give the conditional probability that the gold coin was chosen from box A. Give the conditional probability that the gold coin was chosen from box B. Give the conditional probability that the gold coin was chosen from box C. Give the conditional probability that the gold coin was chosen from box D. c [extra credit 15 points] Let the gold coin remain in your hand. Suppose you get to select a second coin from the same box as you drew the gold coin from. What is the conditional probability that this second coin is also gold? You do not need to make a formal argument, but give the logic you use to come up with your