Assessing petroleum systems using deterministic basin modeling techniques is nowadays widely used in exploration. Decision makers need to rely on the outcomes of basin models whose main results should therefore feature a probabilistic distribution expressing the associated risk. Basin modeling aims at accounting as rigorously as possible for the impact of the numerous parameters controlling petroleum systems, including their subtle coupled effects. Following this, an innovative approach using the experimental design and response surface methodology has been developed and made available within basin modeling tools. The workflow consists first in screening the set of parameters potentially controlling the outcome under evaluation (e.g.: pressure in a targeted reservoir, volume in place) and second in expressing the probability distribution of this outcome taking into account the uncertainty associated to the most influential parameters. This approach is exemplified on a basin model case study from a frontier exploration area of the deep offshore Campos Basin, Brazil.