Given the joint probability and the factored term:
$$ P(S,T,G,F,B) = P(G|B,F) \cdot P(S|T,F) \cdot P(T|B) \cdot P(B) \cdot P(F) $$
I want to compute $P(S = s)$, thus I want to compute
$$\sum_{T,G,F,B} P(S = s, T,G,F,B)$$
Since I want to do the concrete calculation by hand, I would like to eliminate some terms in order to ease the process. Is there anything which could be done? I am thinking of making use of $$\sum_X P(X|Y) = 1$$