When cells are exposed to death ligands such as TRAIL, a fraction undergoes apoptosis and a fraction survives; if surviving cells are re-exposed to TRAIL, fractional killing is once again observed. Therapeutic antibodies directed against TRAIL receptors also cause fractional killing, even at saturating concentrations, limiting their effectiveness. Fractional killing arises from cell-to-cell fluctuations in protein levels (extrinsic noise), but how this results in a clean bifurcation between life and death remains unclear. In this paper, we identify a threshold in the rate and timing of initiator caspase activation that distinguishes cells that live from those that die; by mapping this threshold, we can predict fractional killing of cells exposed to natural and synthetic agonists alone or in combination with sensitizing drugs such as bortezomib. A phenomenological model of the threshold also quantifies the contributions of two resistance genes (c-FLIP and Bcl-2), providing new insight into the control of cell fate by opposing pro-death and pro-survival proteins and suggesting new criteria for evaluating the efficacy of therapeutic TRAIL receptor agonists.