The traditional approaches to program analysis provides semantics based compile-time techniques for statically predicting safe and computable approximations to programs behaviours. We present a quantitative approach to program analysis which provides approximate answers (in a way similar to the classical program analysis) together with some numerical estimate of the approximation introduced by the analysis. Our source for numerical information comes from the use of a probabilistic semantics and in particular of vector space and linear algebraic structures for modelling the computational domain. We then show the usefulness of such an approach for computer security by presenting some applications to the problem of confidentiality, and in particular to the quantitative analysis of systems' confinement.