  We show that the visibility in interference experiments with Bose-Einstein
condensates is directly related to the condensate fraction. The probability
distribution of the contrast over many runs of an interference experiment thus
gives the full counting statistics of the condensed atom number. For
two-dimensional Bose gases, we discuss the universal behavior of the
probability distribution in the superfluid regime and provide analytical
expressions for the distributions for both homogeneous and harmonically trapped
samples. They are non-Gaussian and unimodal with a variance that is directly
related to the superfluid density. In general, the visibility is a
self-averaging observable only in the presence of long range phase coherence.
Close to the transition temperature, the visibility distribution reflects the
universal order parameter distribution in the vicinity of the critical point.
