The Equiprobability Bias in the Monty Hall Dilemma: A Comparison of Primary School, Secondary School, and University Students

The Equiprobability Bias in the Monty Hall Dilemma: A Comparison of Primary School, Secondary School, and University Students Lore Saenen (Lore.Saenen@ppw.kuleuven.be) Methodology of Educational Sciences, KU Leuven, Andreas Vesaliusstraat 2 3000 Leuven, Belgium Mieke Heyvaert (Mieke.Heyvaert@ppw.kuleuven.be) Methodology of Educational Sciences, KU Leuven, Andreas Vesaliusstraat 2 3000 Leuven, Belgium Ilke Grosemans (Ilke.Grosemans@student.kuleuven.be) Methodology of Educational Sciences, KU Leuven, Andreas Vesaliusstraat 2 3000 Leuven, Belgium Wim Van Dooren (Wim.VanDooren@ppw.kuleuven.be) Instructional Psychology and Technology, KU Leuven, Dekenstraat 2 3000 Leuven, Belgium Patrick Onghena (Patrick.Onghena@ppw.kuleuven.be) Methodology of Educational Sciences, KU Leuven, Andreas Vesaliusstraat 2 3000 Leuven, Belgium Abstract The Monty Hall dilemma (MHD) is a notorious brain teaser that received a lot of attention because both novices and statistical experts fail to reason correctly when solving this problem. In the current paper, we try to shed more light on the previous MHD research findings by discussing them in relationship to the equiprobability bias, which is known to develop with age and statistical education. Besides investigating behavioral performances on the MHD, the experiment described in this paper focuses on the level of understanding of the problem and how the latter can be improved. The results show that by increasing the number of alternatives in the MHD, both behavioral performance and understanding of the problem improved. However, full understanding of the MHD was only reached by some participants, and depended on participants’ age and the number of choice alternatives in the MHD. Keywords: Monty Hall dilemma; equiprobability bias; probability; heuristic reasoning; age differences. Introduction The Monty Hall dilemma (MHD) is known as one of the most counterintuitive conditional probability problems. The problem is useful for research in the domain of cognitive psychology because both novices and experts massively solve this problem incorrectly and fail to understand why their reasoning is wrong. The problem is adapted from an American television show called ‘Let’s make a deal’ (Friedman, 1998) and is named after the host of the program. The classic version of the MHD goes as follows: The host, Monty Hall, gives his contestant the option to choose between three identical doors. A prize is randomly placed behind one of the doors. The other two doors conceal mock prizes, for example goats. After the contestant picks an initial door, the host, being aware of the location of the prize, will not yet open this door to reveal what is behind it. Instead, he will first open another door than the door initially chosen by the contestant to show that it contains a mock prize. At this point, when two doors are left unopened, the host asks the contestant to make a final decision. Thus, the dilemma for the contestant is whether to stay with his initial choice for a door, or to swap to the other remaining unopened door. Previous research on the MHD has demonstrated that most people have the idea that winning chances are equal for staying and switching (e.g., Franco-Watkins, Derks, & Dougherty, 2003; Granberg & Brown, 1995). Next, there exists a very strong (cross-cultural) tendency to stay with the initial choice (e.g., Friedman, 1998; Granberg, 1999; Granberg & Brown, 1995). When people solve the MHD for the first time, switching rates vary from 4.5% to 21% (e.g., Bown, Read, & Summers, 2003; Friedman, 1998; Page, 1998). Although the majority of the participants believes that switching and staying hold equal winning chances, they feel more inclined to stay with the initial choice because of the larger amount of regret participants anticipate to experience after a loss due to switching compared to a loss due to staying (Stibel, Dror, & Ben-Zeev, 2009). When applying Bayes’ theorem, however, it becomes clear that the theoretical posterior winning probabilities for staying and switching are unequal. In order to maximize winning chances in the MHD, the best way to proceed is to switch doors because switching yields a 2/3 probability to