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1. (20 points, Pearl 2.1, Darwiche 3.13) There are three urns labeled one, two and three. The urns contain, respectively, three white and three black balls, four white and two black balls, and one white and two black balls. An experiment consists of selecting an urn at random, then drawing a ball from it. (a) (4 points) Define the set of worlds that correspond to the various outcomes of this experiments. Assume you have two variables U with values 1; 2; 3 and C with values black and white. (b) (4 points) Define the joint probability distribution over the set of possible worlds identified above. (c) (3 points) Find the probability of selecting urn 2 and drawing a black ball. (d) (3 points) Find the probability of drawing a black ball. (e) (3 points) Find the conditional probability that urn 2 was selected, given that a black ball was drawn. (f) (3 points) Find the probability of selecting urn 1 or a white ball