[Math Lair] Wason's Four-Card Task

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Starting in the 1960s, Peter Wason studied people's propositional reasoning in a task that he invented called the selection task, or the four-card task. Participants in Wason's experiment would see four cards such as the ones below, with two containing a letter and two a digit. They are told that all four cards have a letter on one side and a digit on the other. They are given the rule "If a card has a vowel on one side, then it has an even number on the other side," and asked to specify those cards, and only those cards, that would allow them to see whether the rule is true.

A D 4 7

Before reading on, think about the one or more cards that you would need to turn over and why, or try an online version of the four-card task on our sister site All Fun and Games.

Now that you've had a chance to think about the problem, the correct task is to select the "A" and "7" cards. Most people get this wrong, usually selecting "A" and "4". The "7" card needs to be turned over since, if there is a vowel on the other side, the rule would be false. On the other hand, regardless of whether there is a vowel or consonant on the other side of the "4" card, it doesn't help to confirm or deny the statement.

If you didn't get the previous problem correct, try the following one: Each card contains a person's age on one side, and what the person is drinking on the other side. Which cards would you need to turn over to verify whether the rule "If a person is drinking a beer, then that person is at least 19 years of age" is true?

drinking a beer drinking a coke 22 years old 16 years old

You probably figured out that you need to flip over the "beer" card and the "16 years old" card. But this problem is the exact same problem as above, only with alcoholic beverages replacing vowels, non-alcoholic ones replacing consonants, overage ages replacing even numbers, and underage ages replacing odd numbers. Why are people who are not able to solve the previous problem able to get this one correct? Most likely the explanation is psychological. R. A. Griggs suggests that the content of the problem brings to mind personal experiences that are relevant to the rule. The latter problem brings to mind experiences that they can draw on, while most people have no real-life experience relevant to reasoning about vowels, consonants, even numbers, and odd numbers.