Question: 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,

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) x2 + y2 < 1/4.
(e) x > y.

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