I focus on probabilistic classification based on linear models and mixture models to find the ones that are the most suitable for the given data. A probabilistic classifier is a mapping that assigns to a vector of features of an object a probability distribution or a model over a set of classes. The probability of a class is a measure of trust that an object belongs to that class. The basic knowledge of probability, Bayes inference. Then, probability classifications with linear and mixed models are based on the estimated parameters from maximum likelihood estimation. Finally, the cross-validation method to compare the models and choose the best one for classification.