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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 ≥ ¼
(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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