Recently, cognitive radio access in time-slotted systems has gained interest. In these systems, the beginning of the slot is used for detection. If no signal is found to be present, remainder of the slot can be used for cognitive radios (secondary users). Detection of the occupancy status of the slots is characterized by false alarm probability and detection probability. The detection probability needs to be large enough to protect primary user. However, too large detection probability means increased false alarm probability thus reducing the secondary users transmit opportunities. We study finding the optimum false alarm and detection probabilities. Numerical results indicate that the secondary users maximum throughput is obtained when the random access probabilities are equal to one and random access is handled instead with false alarm probabilities.