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We consider the problem of sensor selection for time-optimal detection of a hypothesis. We consider a group of sensors transmitting their observations to a fusion center. The fusion center considers the output of only one randomly chosen sensor at the time, and performs a sequential hypothesis test. We study sequential probability ratio test with randomized sensor selection strategy. We present optimal open loop sensor selection policies for three distinct cost functions. We utilize these policies to develop an adaptive sensor selection policy. We rigorously characterize the performance of the adaptive policy and show that it asymptotically achieves the performance of the globally optimal policy.