(a) Let A, B and C be events in the sample space. Suppose that P(B n C) > 0 and P(B'nC) >0. For the following statements determine whether they are true or false and justify your answers. The marks will be awarded for the correct justifications. (i) P(AC) = P(A|BnC) + P(A|Banc) [2 marks] (ii) P(AC) = P(AnB C) + P(AnB'|C) [2 marks] (iii) P(AC) = P(BC)P(A|BAC) + P(B'(C)P(A|B'nC) [2 marks] (iv) If the events B and Care independent then P(AC) = P(B) P(A|BOC) + P(B) P(A|B'n C) [2 marks]