Four cards are presented: A, D, 4, and 7. There is a letter on one side of each card and a number on the other side. Which card(s) must you turn over to determine whether the following statement is false? "If a card has a vowel on one side, then it has an even number on the other side."
This is a classic problem. Carroll discusses the commonly given incorrect solutions and how they relate to confirmation bias, the understanding of logical implications, and what he calls contextual implication.
I still remember this problem from my first day in Introduction to Psychology (the course that was a prereq to all other psych classes). I still give the same answer I did then: You have to check all the cards (or a random sample if presented with a large number of cards) because you cannot rely on a single interpretation of the statement. (Should it be interpreted as a logical ifthen statement, should "if" be interpreted as if and only if, etc?) Normal language is ambiguous, hence the need to invent formal languages to define logical relationships precisely.
Additional thoughts: I've recently been in some discussions on satisficing behavior ... Given that people tend to satifice, it makes sense that many will just check the cards where they see a vowel or an even number. It's a quick solution made with the immediate data on hand, requiring no additional thought about the implications of the statement. So, are people just satisficing? How strong is the relationship between satisficing and confirmation bias?

Ron
2:44 PM