The current article presents the first application of the Generalized Stochastic Microdosimetric Model (GSM2) for computing explicitly a cell survival curve. GSM2 is a general probabilistic model that predicts the kinetic evolution of DNA damages taking full advantage of a microdosimetric description of a radiation energy deposition. We show that, despite the high generality and flexibility of GSM2, an explicit form for the survival fraction curve predicted by the GSM2 is achievable. We illustrate how several correction terms typically added a posteriori in existing radiobiological models to improve the prediction accuracy, are naturally included into GSM2. Among the most relevant features of the survival curve derived from GSM2 and presented in this article, is the linear-quadratic behavior at low doses and a purely linear trend for high doses. The study also identifies and discusses the connections between GSM2 and existing cell survival models, such as the Microdosimetric Kinetic Model (MKM) and the Multi-hit model. Several approximations to predict cell survival in different irradiation regimes are also introduced to include intercellular non-Poissonian behaviors.