The human observer is surprisingly inaccurate in discriminating proportions between two spatially overlapping sets of randomly distributed elements moving in opposite directions. It was shown that observers took into account an equivalent of 74 % of all moving elements when the task was to estimate their relative number, but only an equivalent of 21 % of the same elements when the task was to discriminate between opposite directions. It was concluded that, in the motion direction discrimination task, a large proportion of the signal from all of the elements was inaccessible to the observers, whereas the majority of the signal was accessible in a numerosity task. This type of perceptual limitation belongs to the attentional blindness category, where a strong sensory signal cannot be noticed when processing is diverted by parallel events. In addition, we found no evidence for the common-fate principle, as the ability to discriminate numerical proportions remained the same, irrespective of whether all estimated elements were moving coherently in one direction or unpredictably in opposite directions.