In this study, we discuss a decision theoretic or fully Bayesian approach to the sample size question in clinical trials with binary responses. Data are assumed to come from two binomial distributions. A Dirichlet distribution is assumed to describe prior knowledge of the two success probabilities p ₁ and p ₂. The parameter of interest is p = p ₁ - p ₂. The optimal size of the trial is obtained by maximising the expected net benefit function. The methodology presented in this article extends previous work by the assumption of dependent prior distributions for p ₁ and p ₂.