In this paper, we develop a new scheme to effectively detect the primary signal in a cognitive radio (CR) network. We propose a packet transmission scheme with random censoring. The proposed scheme, known as Censored with Probability Fusion Method~(CPFM), controls the information exchange in cooperative spectrum sensing so as to improve the detection performance and reduce the cooperation overheads. In CPFM, each participating CR device independently senses the spectrum. Based on the energy level received, it may transmit, not transmit, or randomly transmit its observation packet to the fusion centre. The fusion centre then determines the spectrum condition based on all packets received. The simulation results show that CPFM outperforms other detection schemes in terms of improved detection probability and smaller control overheads.