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In this paper, we propose probability-based resource allocation in cognitive radio (CR) networks to exploit the flexibility of opportunistic spectrum access (OSA). Assisted by the statistical information acquired from spectrum sensing, the proposed approach maximizes the overall utility of CR users and ensures sufficient protection of licensed users from unacceptable interference. It also supports diverse quality-of-service (QoS) requirements of multiple CR users and allows distributed implementation. Simulation results demonstrate the effectiveness of the approach as well as its advantage over any conventional approach that ignores the statistical information.