A Consideration of Alternative Sample Spaces Used in Coin-Toss Problems

This paper examines coin-toss comparison questions from two recent studies involving undergraduate students and high school teachers and connects to findings from two prior studies in the literature. Considering possible sample spaces employed by participants, this is a reflection on whether one sequence could be more likely depending on the interpretation of the question. To critique the choice of sequences and determine possible scenarios in which one sequence may be more likely than the other, three alternative sample spaces were explored. It was determined that different sample spaces can lead to one sequence being more likely to occur than the other. Further evaluation discusses whether alternative sample spaces may have been utilised by the participants in each of the studies, and hence, the paper concludes with an advocacy to enquire deeper into participants' reasoning when investigating coin-toss questions.