Empirical support for the Bayesian brain hypothesis, although of major theoretical importance for cognitive neuroscience, is surprisingly scarce. This hypothesis posits simply that neural activities code and compute Bayesian probabilities. Here, we introduce an urn-ball paradigm to relate event-related potentials (ERPs) such as the P300 wave to Bayesian inference. Bayesian model comparison is conducted to compare various models in terms of their ability to explain trial-by-trial variation in ERP responses at different points in time and over different regions of the scalp. Specifically, we are interested in dissociating specific ERP responses in terms of Bayesian updating and predictive surprise. Bayesian updating refers to changes in probability distributions given new observations, while predictive surprise equals the surprise about observations under current probability distributions. Components of the late positive complex (P3a, P3b, Slow Wave) provide dissociable measures of Bayesian updating and predictive surprise. Specifically, the updating of beliefs about hidden states yields the best fit for the anteriorly distributed P3a, whereas the updating of predictions of observations accounts best for the posteriorly distributed Slow Wave. In addition, parietally distributed P3b responses are best fit by predictive surprise. These results indicate that the three components of the late positive complex reflect distinct neural computations. As such they are consistent with the Bayesian brain hypothesis, but these neural computations seem to be subject to nonlinear probability weighting. We integrate these findings with the free-energy principle that instantiates the Bayesian brain hypothesis.