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Suppose you choose two numbers x and y, independently at random from the interval [0, 1]....

Suppose you choose two numbers x and y, independently at random from the interval [0, 1]. Given that their sum lies in the interval [0, 1], find the probability that (a) |x − y| < 1. (b) xy < 1/2. (c) max{x, y} < 1/2. (d) x 2 + y 2 < 1/4. (e) x > y

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