A point (a,b) is chosen from the square R = {0 ≤ a ≤ 1,0 ≤ b ≤ 1}. Suppose that the probability distribution on R is uniform; that is, the probability that a point (a,b) comes from a region in R, equals the area of this region.

(a) Find the probabilities that a ≥ b and 2a ≥ b.

(b) Consider the quadratic equation x² + 2ax +b = 0 with the coefficients (a,b). Find the probability that the equation has real solutions; has only one real solution.