VVe explore the ability to distinguish random from non-random events. Randomness is defined in terms of radioactive decay whereas non-randomness is quantified by excess repetitions (“repeat”) or alternations (“switch”) between successive bits. In the first four experiments no mention was made of randomness, probability, or related concepts in task instructions. Ve found superior performance in distinguishing random stimuli from repeat stimuli compared to switch stimuli. The last three experiments explicitly evoked the concept of randomness, thus allowing comparison of perceptual and conceptual performance. The ability to identify random events from switch distracters was inferior to the ability to discriminate random from switch stimuli. In contrast, for repeat stimuli the concept of randomness appears to roughly coincide with perceptual discriminability. Finally, the ability to identify or produce stimuli as random did not co-vary with the ability to discriminate random from non-random stimuli.