The number of clinical trials that include a binary biomarker in design and analysis has risen due to the advent of personalised medicine. This presents challenges for medical decision makers because a drug may confer a stronger effect in the biomarker positive group, and so be approved either in this subgroup alone or in the all-comer population. We develop and evaluate Bayesian methods that can be used to assess this. All our methods are based on the same statistical model for the observed data but we propose different prior specifications to express differing degrees of knowledge about the extent to which the treatment may be more effective in one subgroup than the other. We illustrate our methods using some real examples. We also show how our methodology is useful when designing trials where the size of the biomarker negative subgroup is to be determined. We conclude that our Bayesian framework is a natural tool for making decisions, for example, whether to recommend using the treatment in the biomarker negative subgroup where the treatment is less likely to be efficacious, or determining the number of biomarker positive and negative patients to include when designing a trial.