The Pope, a nun, Kermit the Frog, and Bruce Lee are all sitting at a bar. Well, actually it's just four people, represented by the cards below.
Each person has an age and a drink type, but you can see only one of these for each person. Here is a rule: "every person that has an alcoholic drink is of legal age." Your task is to select all those people, but only those people, that you would have to check in order to discover whether or not the rule has been violated.
Most people have little trouble picking the correct answer above. But, "across a wide range of published literature only around 10% of the general population" finds the correct answer to the infamous Wason selection task shown below:
Each card has a letter on one side and a number on the other, but you can see only one of these for each card. Here is a rule: "every card that has a D on one side has a 3 on the other." Your task is to select all those cards, but only those cards, which you would have to turn over in order to discover whether or not the rule has been violated.
In fact, Matthew Inglis and Adrian Simpson (2004) found that mathematics undergraduates as well as mathematics academic staff, though performing significantly better than history undergraduates, performed unexpectedly poorly on the task, with only 29% of math undergrads and a shocking 43% of staff finding the correct answer.
In a chapter from The Cambridge Handbook of Expertise and Expert Performance, Paul Feltovich, Michael Prietula, and K. Anders Ericsson indicate the one factor that explains these differential results: knowledge.
Some studies showed reasoning itself to be dependent on knowledge. Wason and Johnson-Laird (1972) presented evidence that individuals perform poorly in testing the implications of logical inference rules (e.g., if p then q) when the rules are stated abstractly. Performance greatly improves for concrete instances of the same rules (e.g., 'every time I go to Manchester, I go by train'). Rumelhart (1979), in an extension of this work, found that nearly five times as many participants were able to test correctly the implications of a simple, single-conditional logical expression when it was stated in terms of a realistic setting (e.g., a work setting: 'every purchase over thirty dollars must be approved by the regional manager') versus when the expression was stated in an understandable but less meaningful form (e.g., 'every card with a vowel on the front must have an integer on the back').
Reference: Inglis, M. & Simpson, A. Mathematicians and the Selection Task. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 2004. (3) 89-96.