The phenomena of behavioral resistance to massive brain damage and behavioral recovery from brain damage suggest there is redundancy in neural tissue. This paper uses basic concepts from probability theory and reliability engineering, as a first step toward more rigorously establishing the plausibility of the redundancy hypothesis. Exponential effects in the relevant formulas lead to results that are intuitively surprising. Thus, within a broad range of parametric assumptions related to lifespan and number of neurons or neural subsystems, it appears that the human brain may be at least twice as large as it would have to be for short-term survival. Simple reliability models suggest that redundancies are in parallel connections of smallest subsystems, such as individual neurons. Other implications of the basic formulas concern the relation between backed-up subsystem reliability and lifetime usage frequency for each subsystem, and the evolution of approximately equal allocation of lifetime reliability among components of a system. In addition, the paper briefly reviews more complex reliability engineering approaches. Redundancy as a reason for neural mass action is compared to other theoretical reasons for mass action in sensorimotor function and learning. Relationships of the present hypothesis to other theories of recovery from brain damage and to theories of regressive trophic phenomena in ontogeny are briefly discussed; it is suggested that as stages of ontogeny progress, both redundancy and flexibility in simpler behavioral functions are traded away for a larger, more differentiated repertoire of complex functions and memories.