Performance on problems included in the fourth administration of NAEP suggest that roughly half of secondary students believe in the independence of random events. In the study reported here about half of the subjects who appeared to be reasoning normatively on a question concerning the most likely outcome of five flips of a fair coin gave a logically inconsistent answer on a follow-up question about the least likely outcome. In a second study, subjects were interviewed about various aspects of coin flipping. Many gave contradictory answers to closely related questions. We offer two explanations for inconsistent 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 explanation, 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 appear when these beliefs are applied beyond their appropriate domain.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education