Visualizing Chance: Tackling Conditional Probability Misconceptions

  • Stephanie BudgettEmail author
  • Maxine Pfannkuch
Part of the ICME-13 Monographs book series (ICME13Mo)


Probabilistic reasoning is essential for operating sensibly and optimally in the 21st century. However, research suggests that students have many difficulties in understanding conditional probabilities and that Bayesian-type problems are replete with misconceptions such as the base rate fallacy and confusion of the inverse. Using a dynamic pachinkogram, a visual representation of the traditional probability tree, we explore six undergraduate probability students’ reasoning processes as they interact with this tool. Initial findings suggest that in simulating a screening situation, the ability to vary the branch widths of the pachinkogram may have the potential to convey the impact of the base rate. Furthermore, we conjecture that the representation afforded by the pachinkogram may help to clarify the distinction between probabilities with inverted conditions.


Bayesian-type problems Conditional probability Dynamic visualizations 



This work is supported by a grant from the Teaching and Learning Research Initiative (


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Authors and Affiliations

  1. 1.Department of StatisticsThe University of AucklandAucklandNew Zealand

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