Eight pigeons were trained on a delayed presence‐versus‐absence discrimination paradigm in which a sample stimulus was presented on some trials but not on others. If a sample was presented, then a response to one choice key produced food. If no sample was presented, a response to the other choice key produced food. The basic finding was that performance remained constant and well above 50% correct on no‐sample trials as the retention interval increased, whereas performance dropped precipitously (to below 50% correct) on sample trials. In the second phase of the experiment, all of the trials were no‐sample trials, and reinforcers were delivered probabilistically for one group of pigeons and according to time‐based schedules for the other group. The exact reinforcement probabilities used in Phase 2 were those calculated to be in effect on no‐sample trials in Phase 1 (according to a discrete‐state model of performance). Subjects did not show exclusive preference for the richer alternative on no‐sample trials in the first phase, but those in the probabilistic group developed near‐exclusive preference for the richer alternative during the second phase. These data are inconsistent with the predictions of the discrete‐state model, but are easily accommodated by an account based on signal detection theory, which also can be applied effectively to discrimination of event duration and the “subjecti