Overcoming illusory inferences in a probabilistic counterintuitive problem: the role of explicit representations

In the context of conditional probabilities, a good example of the marked discrepancy between intuition and formal reasoning is the Monty Hall dilemma (MHD). We used the MHD to study the effects of practicing the game, making explicit the underlying structure, or enhancing the representation of the different possibilities, on reaching and stating the correct answer. The results of the experiments showed that accumulated experience with the MHD increased the proportion of switching responses but did not change erroneous intuitions (Experiment 1). However, when the dilemma was presented in the form of an adversary game that made the underlying structure more explicit, more participants formed complete mental representations that enabled them to reason correctly (Experiment 2). This result was observed even without any practice with the game if the participants were encouraged to represent possibilities (Experiment 3). Therefore, in this context, correct reasoning seems to depend more on the ability to consider different possibilities than on extensive practice with the game.