Choose independently two numbers b and c at random from the

Question

1. Choose independently two numbers B and C at random from the interval [0,1] with uniform density. (This means that the point (B, C) is then chosen at random in the unit square. An event involving the rv's B,C is then a subset of the unit square, and its probability is just the area.)

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.
(f) B < 1/2 and 1- C < 1/2.
(g) conditions (c) and (f) both hold.
(h) B² + C² < 1/2.
(i) (B - 1/2)² + (C-1/2)² < 1/4.