Current curricular guidelines for probability at Primary school level imply the need for a specific training of prospective teachers, which should be based on the previous assessment of their training needs. In order to contribute to this need, in this paper we present the analysis of responses by 157 Spanish prospective teachers to an open question, taken from previous research on subjective perception of randomness. The results show a mixture of correct and wrong conceptions, some of which parallel some historical conceptions of randomness. Teachers’ educators could start from these intuitions to help prospective teachers advance to a broader meaning of the concept, adequate for their future teaching responsibility.