Tumor development is characterized by a compromised balance between cell life and death decision mechanisms, which are tightly regulated in normal cells. Understanding this process provides insights for developing new treatments for fighting with cancer. We present a study of a mathematical model describing cellular choice between survival and two alternative cell death modalities: apoptosis and necrosis. The model is implemented in discrete modeling formalism and allows to predict probabilities of having a particular cellular phenotype in response to engagement of cell death receptors. Using an original parameter sensitivity analysis developed for discrete dynamic systems, we determine variables that appear to be critical in the cellular fate decision and discuss how they are exploited by existing cancer therapies.