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A point (x, y) is to be selected from the square S containing all points (x, y) such that 0 ? x ? 1 and 0 ? y ? 1. Suppo

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A point (x, y) is to be selected from the square S containing all points (x, y) such that 0 ? x ? 1 and 0 ? y ? 1. Suppose that the probability that the selected point will belong to each specified subset of S is equal to the area of that subset. Find the probability of each of the following subsets: (a) the subset of points such that (x ? 1 2 )2 + (y ? 1 2 )2 ? 1 4 ; (b) the subset of points such that 1 2 < x + y < 3 2 ; (c) the subset of points such that y ? 1 ? x2; (d) the subset of points such that x = y.

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