Nobody gets it. Investigating posterior probability reasoning in the Monty Hall dilemma

Although probabilities are central both to statistical education and to dealing with uncertain events in real-world situations, a good understanding of the concept of probability itself is not straightforward. Understanding probabilities may become even more difficult when conditional information has to be taken into account. The aims of the present dissertation are to further investigate how people reason about posterior probabilities and to examine why a correct understanding of posterior probabilities is so difficult. Regarding the domain of posterior probabilities, one of the most counterintuitive problems is the Monty Hall dilemma (MHD). Because of the many emotional and cognitive processes that are involved when people solve this problem, the MHD was used as the common task in the various studies we performed and will be reported in this dissertation.

Chapter 1 presents a systematic literature review we conducted on the question addressing why participants fail to perform well on the MHD and to understand its solution. More specifically, the systematic review investigated why humans fail to solve the MHD, which individual differences are related to humans’ MHD performance, and whether humans’ performance on the MHD can be improved. In the systematic review, the role of participants’ working memory capacity and their distorted memory for outcome/decision frequencies were discussed. These findings served as the inspiration for the study reported in Chapter 2, which examined the effect of external help on participants’ MHD performance. In Chapter 3 and Chapter 4, the role of participants’ age on their MHD performance was investigated, as the systematic review of Chapter 1 revealed a lack of research with non-adult participants. The study in Chapter 3 focused on the relationship between participants’ age and the equiprobability bias. Next, the study in Chapter 4 focused on participants’ justifications for their MHD performance in order to get a deeper understanding of participants’ reasoning about posterior probabilities. Chapter 5 contains an intervention study in which participants used an MHD digital learning environment. This study was set up in order to reveal which (combination of) manipulation(s) helped participants most in understanding the MHD solution. The dissertation ends with a general conclusion and discussion in Chapter 6 in which we critically look back at the main results of our studies, make some methodological considerations, and discuss both theoretical and practical implications of our findings.