9. Take three events A, B, and C, and assume that A is independent of B and C, and B is independent of C. Of course, these statements imply: P(A ['1 B) = P(A)P(B) (1) P(A H C) = P(A)P(C') (2) P(B n C) = P(B)P(C). (3) Does it also imply: P(A O B n C) = P(A)P(B)P(C). (4) If it does, show how (1), {2), (3) imply (4), and if it doesn't, give a full counter example. '10 pts: 5 I a