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In wireless sensor networks (WSNs), key management is one of the crucial aspects of security. Although existing key management schemes are enough to solve most of the security constraints on WSNs, a random-key predistribution scheme has recently evolved as an efficient solution for sharing keys between sensor nodes. Studying the signal ranges of the sensor nodes might significantly improve the performance of the key-sharing mechanism, but this possibility remains unexploited and needs further attention. Hence, in this paper, we propose a new approach for a probabilistic key predistribution scheme that guarantees a higher probability of sharing keys between nodes that are within the signal range than that of other schemes. As a result, the proposed approach provides adequate security and is expected to minimize the key ring, reduce the communication overhead, and provide high connectivity. We also compare our present scheme with existing algorithms developed for the same purpose and observe that the proposed scheme performed better, even with different deployment errors.