Let (X, Y) denote a uniformly chosen point in the unit square [0, 1]²= {(x, y): 0 < x, y ≤ 1}. 1. Let 0 ≤ a < b ≤ 1. Find the probability P(a < X < b). 2. Find P(|X – Y| ≤ 1/4). Define the probability space (N, F, P) in this case. (No need to specify what F is, you may assume it is the Borel sets of [0, 1]²).

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