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A BBN is a compact representation of the Joint Probability Distribution (JPD) defined by its associated variables. Once you get this JPD, inference in a BN is simply computing a conditional probability of some subset of variables in the network, conditioned on another subset. For small models ( <10 binary variables) this is a trivial. In general, the "what is computed" is straightforward, but impractical by brute force. The "how it is computed" is the subject of a large public literature on propagation and approximation methods.