This work presents an airfoil probabilistic design methodology for wind energy applications, using an analytical approach to estimate the angle-of-attack fluctuations produced by non-uniformities in the incoming wind field. The contemplated wind speed perturbations include wind shear, yaw misalignment and atmospheric turbulence, and several combinations of the perturbation sources are considered. A probabilistic design space mapping is carried out to evaluate which wind conditions occur more often in practice and how likely each specific combination of perturbation sources is to occur, for both an onshore and offshore scenario. The proposed probabilistic method and specifically the level of angle-of-attack fluctuations is verified by employing the aero-elastic simulation tool FAST for each case. Finally, the probabilistic approach is used to design airfoils sections employing the genetic multi-objective airfoil optimization tool Optiflow, where the probability of angle of attack fluctuations for a given scenario is used to prescribe the operational angle of attack range over which the airfoil performance is relevant. Results of the airfoil optimization for a 24% thick section are presented, illustrating the trends in foil geometry and aerodynamic performance for three different possible optimization objective functions.