# Bayes Network. Is possible to calculate without all joint distributions?

I have the following Bayes network

Is it possible to get probability of P(X|ABC) if I have only the probabilities P(X|A), P(X|B), P(X|C) ?

Thanks.

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No it is not. You are welcome. –  Did Sep 15 '12 at 14:25

Are A, B and C independent based on the network diagram? If so P(X|ABC)=P(XABC)/P(ABC)=

P(XABC)/[P(A) P(B) P(C)] = P(XBC|A)/[P(B) P(C)] =P(XAB|C)/[P(A) P(B)]=P(XAC|B)/[P(A) P(C)].

So you need to know two of these 3 probabilities P(A) P(B) and P(C) along with the appropriate one from P(XAB|C), P(XBC|A) and P(XAC|B).

You can't get these probabilities directly from knowing P(X}A) P(X|B) and P(X|C).