The Venn diagram shown is for an experiment with sample space S = {1,2,3,4,5,6,7,8} and events A, B, C, and D. a) For each of the following, write the letter (A, B, C, or D) of the event described. Write "X" if the event described is not A, B, C, nor D. 6 . Event is outcomes less than 4. . Event is outcomes between 5.2 and 6.8 . Event is NOT even outcomes. . Event is non-zero powers of 2 (i.e. 2* where x * 0). b) Are A and B mutually exclusive [Y or N]? c) Are B and C mutually exclusive [Y or N]? d) Are B and D mutually exclusive [Y or N]? e) List the elements of A U B. f) List the elements of B n C. g) List the elements of (C n D) U A. h) Using only events A, B, C, and D, give a list of events that partition the sample space S. i) Assume that all outcomes are equally likely [i.e. P(1) = P(2) = P(3) = ... = P(8)]. Determine the following: P(D) = P(C' U B) = P(B') = P(C' n B) = j) Now, assume all even outcomes are equally likely [i.e. P(2) = P(4) = P(6) = P(8)] and that all odd outcomes are equally likely [i.e. P(1) = P(3) = P(5) = P(7)], but an even outcome is not necessarily equally likely to on odd outcome. Additionally, it is known that P(C n D) = 0.3. Determine the following: P(A) = P(D) = P(C) = P(C U D) =