  Differential privacy is achieved by the introduction of Laplacian noise in
the response to a query, establishing a precise trade-off between the level of
differential privacy and the accuracy of the database response (via the amount
of noise introduced). Multiple queries may improve the accuracy but erode the
privacy budget. We examine the case where we submit just a single counting
query. We show that even in that case a Bayesian approach may be used to
improve the accuracy for the same amount of noise injected, if we know the size
of the database and the probability of a positive response to the query.
