Early Phase II clinical trials typically have a biomarker as a primary outcome. The extent to which a positive result for such a Phase II trial is predictive for Phase III success is of obvious concern. In this article we extend existing approaches for assessing the probability of success in Phase III. We address the case that a dichotomous clinical endpoint of interest is to be measured in Phase III. A Beta prior distribution is suggested that quantifies information from both the data observed on the biomarker and its predictive accuracy. Based on the quantification of the impact of the predictive ability of biomarkers, it is shown that the predictive quality of a biomarker needs to be substantial to support the full development decision. The approach is illustrated with a practical example. A simulation study is presented to illustrate the findings more generally.