Suppose that a second ball is drawn from the urn, without replacing the first. Let Y₂ = 1 if the second ball is red, and let it be 0 otherwise. Use the posterior distribution of X from the previous question as the prior distribution for X. Suppose the second ball is green. Find the posterior distribution of X by filling in the simplified table:

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X prior likelihood prior x likelihood posterior marginal P(Y2 = 0)