Question 1 (10 points) Consider the following probability distributions: ABP(BA) B|C| P(C|B) AP(A) tt 0.9 t t 0.8 CDP(D|C) t|t 0.25 t 0.8 tf 0.1 t f 0.2 t f 0.75 f 0.2 ft 0.6 ft ff 0.4 ff 0.8 0.2 ft 0.5 ff 0.5 Given just these tables and no independence assumptions, calculate the following probabilities, showing your work. If it is impossible to calculate without more independence assumptions, specify instead a minimal set of independence assumptions that would allow you to answer the question. a) P(a,b) (2 points) b) P(b) (2 points) c) P(-a, -b, c) (2 points) d) Now assume C is independent of A given B and D is independent of A and B given C. e) Calculate P(a, b, c, d) (4 points)

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