Abstract
This research continues the longstanding tradition of investigating relative likelihood comparisons. Respondents are presented with sequences of heads and tails derived from flipping a fair coin five times, and asked to consider their chances of occurrence. An iteration of the task, which maintains the ratio of heads to tails in all of the sequences presented, provides unique insight into individuals’ normatively incorrect relative likelihood comparisons. In order to reveal the aforementioned insight, this research, based upon participants’ response justifications, presents unconventional partitions of the sample space, which are organized according to switches, longest run and switches and longest run. In doing so, it will be shown that normatively incorrect responses to the task are not necessarily devoid of correct probabilistic reasoning. To accurately render the data gathered from 239 prospective mathematics teachers, an original theoretical framework (the meta-sample-space) will be used with a new method (event-description-alignment) to demonstrate, that is model, that certain individuals base their comparisons of relative likelihood according to a subjective organization of the sample space, that is, a subjective-sample-space.
