Quorum systems-collections of sets with pairwise nonempty intersections-are used in distributed settings to implement services such as consensus and consistent memory. Quorums have been substantially studied in static settings, however the design and analysis of quorum-based distributed services in resource-limited ad hoc networks is a relatively unexplored area. The pioneering work of Chockler, Gilbert, and Patt-Shamir  considers such networks and proposes an implementation of probabilistic quorum systems with per-node communication bit complexity of O (log2 n), where n is the number of nodes. The authors assumes a priori knowledge of node failure probability p, where 0 ≤ p < 1/4. Additionally their work overlooks the cost of gathering responses from quorum members by the client. We present a new probabilistic quorum construction with a lower, per quorum access, communication bit complexity of O (logn) for multi-hop networks. Our quorum access algorithm is based on self-sampling by the nodes themselves, in a way equivalent to accessing a quorum set, with high probability. In addition, we provide a novel on-line algorithm to estimate the node failure probability parameter p, thus removing the assumption that it is known a priori. This is accomplished with per node communication bit complexity of O (log2 n). We demonstrate the utility of our construction by presenting a single-writer, multi-reader algorithm that uses our probabilistic quorums to implement atomic objects in ad hoc networks, where consistency is guaranteed with high probability. We include simulation results illustrating the high probability guarantee for our atomic memory service.