This paper describes a study in which subjects were asked about various aspects of coin flipping. Many gave contradictory answers to closely-related questions. We offer two explanations for such responses: (a) switching among incompatible perspectives of uncertainty, including the outcome approach, judgment heuristics, and normative theory; and (b) reasoning via basic beliefs about coin flipping. As an example of the latter, people believe both that a coin is unpredictable and also that certain outcomes of coin flipping are more likely that others. Logically, these beliefs are not contradictory; they are, however, incomplete. Thus, contradictory statements (and statements at variance with probability theory) appear when these beliefs are applied beyond their appropriate domain.