Suppose that a point (x, y) is chosen from the unit square S = [0,1]×[0,1] using the uniform probability law — the probability that (x, y) is in a subset A of S is equal to the area of A:
P ((x, y) ∈ A) = area(A) for all A ⊂ S.
(a)What is the probability that x + y <1/3 ?
(b)What is the probability that x + y <3/2 ?
(c)Find an algebraic expression F(u) for
F(u) = P (x + y ≤ u).