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Consider two urns, labelled urn #1 and urn #2. Suppose, as in Exercise 1, that urn #1 has 5 red…

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 Consider two urns, labelled urn #1 and urn #2. Suppose, as in Exercise 1, that urn #1 has 5 red and 7 blue balls, that urn #2 has 6 red and 12 blue balls, and that we pick three balls uniformly at random from each of the two urns. Conditional on the fact that all six chosen balls are the same color, what is the conditional probability that this color is red?