Suppose that a point is picked at random from the unit square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1.

Let A be the event that it falls in the triangle bounded by the lines y = 0,x = 1, and x = y, and let B be the event that it falls into the rectangle with vertices (0, 0),(1, 0),(1, 1/2), and (0, 1/2). Find all statements that are true: (i)

P(A) = P(B). (ii) P(A ∩ B)=3/8. (iii) P(A ∪ B) = P(A ∩ B). (iv) A and B are independent. (v) P(A|B)=1/8.