We investigate the consequences of natural conjectures of Montgomery type on the non-vanishing of Dirichlet L-functions at the central point. We first justify these conjectures using probabilistic
arguments. We then show using a result of Bombieri, Friedlander and Iwaniec, and a result of the author that they imply that almost all Dirichlet L-functions do not vanish at the central point. We also deduce a quantitative upper bound for the proportion of Dirichlet L-functions for which L( 1/2, χ) = 0.