This work reports the results of an investigation that aimed to know the informal reasoning of high school students with and about the frequency approach of probability and the law of large numbers when they were faced with a problem about random intervals. The research question was as follows: What features of students' reasoning about the frequency approach of probability are revealed when they solve a task on random intervals? To advance the answer, an activity was carried out involving students between ages 16 and 17 who built random intervals through manipulative and computational simulations, the latter with the software Fathom. In addition, they were provided with a worksheet with questions for them to express their reasoning. Their responses were coded and ranked. At the end, we summarize the results and highlight prediction and variability as essential features to understand the frequency approach to probability.