This study concerns the effect of uncertain tooth profile modifications on the primary resonance of a spur gear pair induced by the backlash nonlinearity. It should be noted that these corrections are micro geometric within tolerances. This primary resonance can exhibit dynamic responses with vibro-impacts between teeth. In this context, we have developed an original approach based on tracking the saddle-node bifurcations of the primary resonance. The equation of motion is solved using the harmonic balance method combined with an arclength continuation method and a bordering technique. The control parameters are the meshing frequency associated with the rotation speed, and the tip relief associated with the profile correction. The evolution of the bifurcation points with respect to the parameters is calculated deterministically. To characterize the severity of the resonance, we introduce two criteria, namely the amplitude of the response at the resonance peak and the width of the resonance hysteresis. Uncertainty is then introduced by means of probability densities of the tip relief within the tolerance interval. Monte Carlo simulations are then used to conclude on the optimum profile correction, which differs significantly from that recommended in the purely deterministic case.