Choose independently two numbers B and C at random from the interval [0, 1] with
uniform density. Prove that B and C are proper probability distributions.
Note that the point (B,C) is then chosen at random in the unit square.
Find the probability that
(a) B + C < 1/2.
(b) BC < 1/2.
(c) |B − C| < 1/2.
(d) max{B,C} < 1/2.
(e) min{B,C} < 1/2.
