Both intensional and extensional background knowledge have previously been used in inductive problems to complement the training set used for a task. In this research, we propose to explore the usefulness, for inductive learning, of a new kind of intensional background knowledge: the inter-relationships or conditional probability distributions between subsets of attributes. Such information could be mined from publicly available knowledge sources but including only some of the attributes involved in the inductive task at hand. The purpose of our work is to show how this information can be useful in inductive tasks, and under what circumstances. We will consider injection of background knowledge into Bayesian Networks and explore its effectiveness on training sets of different sizes. We show that this additional knowledge not only improves the estimate of classification accuracy it also reduces the variance in the accuracy of the model.