In this thesis, we address the problem of estimating count queries on databases quickly, without accessing the database at query time. We accomplish that by building a model of the domain from the database in a preprocessing phase, and use this to answer count queries. The model we use is the Mixture Model of Bayesian Networks (MMBN), which effectively encodes the joint probability distribution of the domain. An MMBN is a weighted model with Bayesian Networks (BNs) as components. We describe how to learn an MMBN model from a database using an instance of the modified Expectation-Maximization (EM) algorithm, called EAM algorithm, and evaluate its accuracy on real and artificial data sets. Experimental results show that MMBNs can represent a data set satisfactorily and can approximate counts with the high degree of accuracy, without accessing the database.