3. Show that if A, B, and C are mutually independent, then A", B and C are also mutually independent. 4. (Definition of independence) This question helps you to understand the definition of in- dependence for more than 2 events. Consider 3 independent events A, B and C of the sample space S. H (a) Write down the definition of A, B and C being independent (the answer is in the lecture notes). (b) Show that P(A|BOC) = P(A). (c) Show that P(C|AU B) = P(C). (d) Show that P(B|(An C)") = P(B). (e) Show that P(B n A.(C) = P(B)P(A")