In this letter, a Monte-Carlo approach is proposed to tackle the control design problem of coadministration of propofol and remifentanil during the induction phase of total intravenous anesthesia, where the measured output is the Bispectral Index (BIS). The goal is to minimize the expected value of the Integral Absolute Error of the BIS in presence of high model uncertainties. An additional constraint is used in the resulting optimization problem to limit the probability of a large undershoot of the BIS signal. Simulation results validate the proposed methodology and provide a comparison between the proposed method and another one from the literature.