Random sampling and random allocation are essential processes in the practice of inferential statistics. These processes ensure that all members of a population are equally likely to be selected, and that all possible allocations in an experiment are equally likely. It is these characteristics that allow the validity of the subsequent calculations that use probabilistic reasoning. This paper suggests that despite the importance of these processes, students may poorly understand the characteristics of these processes, and the reasons for them. The paper concludes with suggestions for the improvement of teaching these topics.