4.5.8 Suppose that a point is picked at random from the unit square 0 5 z 5 1,0 5 y 5 1. Let A be the event that it falls in the triangle bounded by the lines y =

0,z = 1, and z = y, and let B be the event that it falls into the rectangle with vertices (O,O), ( l , O ) , (1,1/2) and (0,1/2). Find all statements that are true: (i)

P ( A U B ) = P ( A n B ) . (ii) P(A1B) = 1/8. (iii) A and B are independent. (iv)

P(A)= P(B) .( v)P (An B) = 318.