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(AnB) = P(A) P(B) P(AnC) = P(A) P(C) P(BOC) = P(B) P(C). Does it also imply: P(AnBnC) = P(A) P(B) P(C). If it does, show how (1), (2), (3) imply (4), and if it doesn't, give a full counter example. (10 pts)