In this paper, we investigate the ways in which 15 year-old students conceive interrelated issues of randomness. We deal with these issues of randomness as a whole and not separately from each other, in contrast to the research so far. In order to analyse the students' ways we introduce a modification of Kyburg's Schema [(1974). "The logical foundations of statistical inference." Boston: Reidel] for subjective interpretation of randomness, together with the notion of a student's "potential world" as a new theoretical framework. This last notion comprises all views, beliefs and ideas a student has at a specific time about the notion of randomness, which have been formed from his/her individual interpretation of experiences. Our analysis of responses from students' interviews reveals that few students conceive the notions of randomness in a uniform way, while the rest of them conceive these notions in different ways. It turns out that this variety of students' conceptions depends heavily on their own "potential worlds," which are grounded on social, personal or institutional sources.