Four card solution

Obviously we need to turn over the D to check that there is a 3 on the back (everybody gets this one right). And equally obviously, there’s no need to turn over the K (and again, everybody realises this). The 3 card is a tricky one. Most people think that you need to turn this card over to see whether there is a D on the other side. This would be necessary had the claim been that “Every card that has a D on one side has a 3 on the other, and vice versa”. But it wasn’t. The 7 is the other tricky one. It doesn’t occur to most people that we need to turn this card over to check that the letter on the back is not D. If it is D, then the claim is false.

This trick illustrates the phenomenon of confirmation bias. Most people, being fairly charitable sorts, want to turn over the 3, find a D on the back and confirm the claim (“Well done, you’re right!”). And so it is with homeopathy (or conspiracy theories). People who want to believe that the treatment works actively search for opportunities to confirm this belief, focusing on homeopathy patients who seem to have got better (“3 cards”) and reject opportunities to disconfirm it, by ignoring research studies (“7 cards”).

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