Fully auditory Brain-computer interfaces based on the dichotic listening task (DL-BCIs) are suited for users unable to do any muscular movement, which includes gazing, exploration or coordination of their eyes looking for inputs in form of feedback, stimulation or visual support. However, one of their disadvantages, in contrast with the visual BCIs, is their lower performance that makes them not adequate in applications that require a high accuracy. To overcome this disadvantage, we employed a Bayesian approach in which the DL-BCI was modeled as a Binary phase shift keying receiver for which the accuracy can be estimated a priori as a function of the signal-to-noise ratio. The results showed the measured accuracy to match the predefined target accuracy, thus validating this model that made possible to estimate in advance the classification accuracy on a trial-by-trial basis. This constitutes a novel methodology in the design of fully auditory DL-BCIs that let us first, define the target accuracy for a specific application and second, classify when the signal-to-noise ratio guarantees that target accuracy.