The aim of this study was to predict drivers' drowsy driving and stop drivers from driving under drowsy states. While the participants were required to carry out a simulated driving task, EEG (MPF and α/β-ratio), ECG (RRV3), tracking error, and subjective rating of drowsiness were measured. On the basis of such measurements, we made an attempt to predict the decreased arousal level using Bayesian estimation which is generally used to estimate the cause on the basis of the effect (in this case, the measurements above). As a result of predicting the decreased arousal level using MPF, α/β-ratio, and RRV3, it has been suggested that the drowsy driving represented by larger tracking error during the simulated driving can be predicted in advance. Moreover, the proposed prediction method enabled us to predict the point in time when the participant surely encountered a serious accident with fairly high probability. It was also found that the fine renewal of the prior probability lead to the decrease of false prediction of decreased arousal level.