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Peer-to-peer (P2P) system is an overlay network of peer computers without centralized servers, and many applications have been developed for such networks such as file sharing systems. Because a set of peers dynamically changes, design and verification of efficient protocols is a challenging task. In this paper, we consider an object searching problem under a resource model such that there are some replicas in a system and the lower bound of the ratio ρ=n'/n is known in advance, where n' is a lower bound of the number of peers that hold original or replica for any object type and n is the total number of peers. In addition, we consider object searching with probabilistic success, i.e., for each object search, object must be found with at least probability 0<σ<1. To solve such a problem efficiently, we propose a new communication structure, named probabilistic weak quorum systems (PWQS), which is an extension of coterie. Then, we propose a fault-tolerant protocol for searching for objects in a P2P system. In our method, each peer does not maintain global information such as the set of all peers and a logical topology with global consistency. In our protocol, each peer communicates only a small part of a peer set and, thus, our protocol is adaptive for huge scale P2P network.