The probability of failing processors in the multiprocessor system increases as the cardinality of system grows. The subsystem reliability in a system, defined as the probability that a subsystem of a specified cardinality is operational with the emergence of failed nodes. In this paper, we derive an approximation and an upper bound on the probability of a subgraph Dn−1 being fault-free under the probabilistic fault model. Numerical simulations indicate that these two analytical results we get are in good consistency, especially when the node reliability is at a low level.