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Radio frequency identification (RFID) represents one of the most important innovations of the last decades for the management of supply chains and for goods tracking. However, an important question in RFID systems concerns the time needed for completing the identification of multiple clients that try to access the shared medium simultaneously. Several approaches have been proposed for implementing medium access control (MAC) protocols for RFID systems; among them, the binary tree protocol represents a very efficient solution, also included in the ISO standard for RFID. However, in order to be implemented, the binary tree protocol needs a suitable bit coding of the client identifiers and a centralized coordination of the medium contention phase. In this paper, we consider instead a very simple stochastic protocol that implements a distributed version of binary tree. It is shown that such protocol is able to achieve the same performance of classic binary tree, without needing any bit coding nor centralized coordination. Numerical simulations show that the performance achievable can be favorably compared with that of other solutions for small and medium size sets of tags, that is a frequent condition in practical applications.