4. [25 pts] You are given the following information on Events A, B, C, and D. P(A) = .4 P(A UD) = .6 P(B) = .2 P(A | B) = .3 P(C) = .1 P(An C) = .04 P(A n D) = .03 a) [3 pts] Compute P(D). b) [3 pts] Compute P(A n B). c) [4 pts] Compute P(A | C). d) [3 pts] Compute the probability of the complement of C. e) [3 pts] Are A and B mutually exclusive? Explain your answer. f) [3 pts] Are A and B independent? Explain your answer. g) [3 pts] Are A and C mutually exclusive? Explain your answer. h) [3 pts] Are A and C independent? Explain your