While Advanced Driver Assistance Systems (ADAS) are becoming the longer the more common, most interest has been devoted either to highway traffic or to special situations like parking. Against this background, this paper focuses on overtaking maneuvers on country roads, and a stochastic model predictive control (MPC) algorithm is implemented to manage this task. The behavior of the surrounding vehicles is predicted stochastically by using Bayesian networks. The overtaking algorithm is tested for various country road traffic scenarios in a stochastic traffic environment. To compare the performance of the controller to that of a real human driver a dedicated study in this stochastic traffic environment is carried out. The results of this study show that the control algorithm provides the safest trip in acceptable travel time.