Sensing-throughput trade off has widely been investigated in cognitive radio networks. Detection probability and interference ratio are usually considered the main constraints to the protection of primary signals. However, the detection probability defined during a sensing duration does not fully capture the goal of primary protection because two important factors are not taken into consideration. Neither the detection latency during the detection of the primary signal nor the unavoidable mis detection of the primary signal due to its ability to only occupy the channel between two consecutive sensing durations are considered. Motivated by these problems, the authors propose a new detection probability called the Time-constrained Detection Probability (TDP) and investigate the effect of the sensing interval on the TDP.