In this literature review, we survey student naïve ideas (frequently referred to as 'misconceptions') that plausibly relate, at least in part, to difficulty in understanding probability. We collected diverse naïve ideas from a range of topics in physics: Non-linear Dynamics; Cosmology; Thermal Physics; Atomic, Nuclear, and Particle Physics; Elementary Particle Physics; Quantum Physics; and Measurements and Uncertainties. With rare exception, these naïve ideas are treated in the literature to be topic-specific. For example, the idea that 'only one measurement is needed because successive measurements will always yield the same result' is treated to be a misconception in Measurements and Uncertainties. In our review, however, we raise the possibility that these diverse naïve ideas have something in common: they are enabled, to varying degrees, by the stance that 'random is incompatible with predictions and laws' that researchers in mathematics education have documented. This is important, as it may inform instruction. Namely, it may be the case that it is more effective to treat this underlying cause of student difficulty, rather than the individual naïve ideas themselves.