Consider the following probability distributions: 

Given just these tables and no independence assumptions, calculate the following probabilities, showing your working. 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). 

b. P(b). 

c. P(¬a, ¬b, c). 

d. Now assume C is independent of A given B and D is independent of A and B given C. Calculate P(a, ¬b, c, d).

A P(A) t 0.8 f 0.2 ABP(BA) 0.9 0.1 0.6 0.4 tt tf ft ff BCP(CB) 0.8 0.2 tt tf ft ff 0.8 0.2 CDP(DC) 0.25 0.75 tt t f ft ff 0.5 0.5