In a box of gadgets containing 3 Samsung phones, 2 iPhones, and 3 Google Pixel phones, a random sample of 4 phones is selected. If X is the number of Samsung phones and Y is the number of iPhones in the sample, find:  a. the joint probability distribution table of X and Y; b. P[(X, Y ) ∈ A], where A is the region that is given by {(x, y) | x + y ≤ 2}. c. f(y|x=2) for all values of y (tabulate); d. P(X = 0 | Y = 2).

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