Performance on problems included in the most recent administration of NAEP suggest that the majority of secondary students believe in the independence of random events. In the study reported here a high percentage of high-school and college students answered similar problems correctly. However, about half of the students 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. It is hypothesized that these students were reasoning according to an "outcome approach" to probability in which they interpreted their task as predicting what actually would occur if they flipped a fair coin five times. This finding suggests that the percentage correct on corresponding NAEP items are inflated estimates of normative reasoning about independence.
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