Poll Question Analysis

Question

Here are some playing cards.

And here is a proposition:

Which card(s) must you turn over in order to test this proposition?

Response

The majority of respondents (36%) thought the answer was (d) All of them.

Interesting.

Very interesting, in fact, because we only need to look at the first card in the list – Card A – to realize that this is incorrect!

Card A shows an even number, and the proposition says absolutely nothing about even numbered cards. The reverse side of Card A could be blue, red, purple, green or even a lovely photograph of the Queen. Turning over this card would neither support nor disprove the proposition.

Let’s look at the remaining cards in turn.

Card B shows an odd number. If the proposition is true, then Card B must be blue on the other side. This is an easy one; we definitely need to turn over Card B to test the proposition. Sadly, this doesn’t help with answering the question, because all of the options (a) to (d) included Card B. Sorry about that.

What about Cards C and D?

This is where it gets a little strange. The reverse of Card C is red, so at first glance it would appear to be irrelevant. Suppose, however, that we turned it over and it showed us an odd number. Wouldn’t that be a direct counterexample to the proposition? It certainly would, because an odd numbered card should be blue on the reverse, not red. We should turn over Card C to check.

Finally, the reverse of Card D is blue. The proposition does indeed mention blue cards, but it only states that odd numbered cards must be blue on the reverse. It does not exclude other cards from being blue on the reverse. Card D could be odd, even, an irrational number like π or a lovely photograph of Boris Johnson. Much like Card A, turning over this card would neither support nor disprove the proposition.

So, to conclude, the correct answer is (b) Cards B and C only.

This problem is known as the Wason Selection Task, named after the English psychologist Peter Cathcart Wason. When Wason originally posed this question in the 1960s, fewer than 10% of test subjects selected the right cards. The test was repeated by other researchers in later years, with much the same success rate.

The reasons for incorrect responses are varied and somewhat complex, but psychologists generally agree that confirmation bias plays a role. Confirmation bias causes us to preferentially seek out information that supports a hypothesis or belief. So, when testing a proposition such as the one above, we have no problem recognizing a card that could support the proposition (Card B), but we are much less inclined to check cards that could disprove it (Card C). Indeed, over a third of respondents were uninterested in Card C. That may be a manifestation of confirmation bias.

Having said that, 27% of respondents did answer our poll question correctly, which is a lot better than the results found by Wason et al. It would thus appear that Facets readers are better than average at logical reasoning (phew).