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Cognitive radio (CR) systems are typically classified into two types. In overlay CR, a secondary user opportunistically accesses primary user's spectrum when it is unused, while a secondary user in underlay CR accesses the spectrum at any time as long as the interference power received at a primary user is below a certain level. This paper investigates a hybrid CR system where a secondary user probabilistically changes its spectrum access mode for secondary user's throughput maximization while guaranteeing primary user's target throughput. Basically, the hybrid CR works like overlay CR. The secondary user constantly monitors activity of the primary user and transmits data with maximum transmit power if transmission of the primary user is not detected. However, the only difference from overlay CR is that even when transmission of the primary user is detected, the secondary users are able to access the spectrum with regulated low transmit power with switching rate c. We show that there is a trade-off of increasing c due to recursive interactions between primary and secondary users, and optimizing c is crucial to balance the gain and loss of secondary user's underlay spectrum access. The proposed hybrid CR is shown to achieve higher throughput and be more robust to detection errors than conventional CR systems.