Abstract
This study aimed to design and analyze activities that enable students to investigate the probabilities of compound events and the equiprobability bias by a perception-based design that foregrounds sample sets. Drawing on historical insights and prior research, we designed activities to guide students in exploring the probabilities of compound events. These activities aimed to encourage students to reconcile their intuitively generated sample sets with formal probability operations. We anticipated that this approach would make their exploration of probabilities more mathematically precise and provide a warrant to convince and justify their solutions. The results demonstrated how students bridge enumeration and probability operations, navigate between these methods to explore the probabilities of compound events, and address issues of order. Additionally, employing a tree diagram mediated the integration of enumeration and probability operations. We also identified three implicit rules generated by students that could influence classical probability exploration. These rules are as follows: enumeration and probability addition or multiplication always yield the same probability, enumeration is always applicable in finding probabilities, and probability can be reduced to enumeration.
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Park, J. Exploring the probabilities of compound events and the equiprobability bias by navigating between enumeration and probability operations. Educ Stud Math 120, 371–395 (2025). https://doi.org/10.1007/s10649-025-10430-z
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DOI: https://doi.org/10.1007/s10649-025-10430-z