This work reports the results of a research aimed to know the probabilistic reasoning of high-school students when they deal with the notion of random intervals. An activity was carried out involving students between ages 16 and 17 who built random intervals through physical and computational simulations. The research question guiding this work was: Which reasoning do students exhibit when they estimate the probabilities of events related to the experience of creating random intervals from a frequentist approach? From the data analysis, partly based on the Grounded Theory, four categories were established. They suggest that the patterns observed in this work are likely present in situations demanding the frequentist approach to probability. [For the complete proceedings, see ED629884.]