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This puzzle appeared in the 'Skeptical Adversaria' (the newsletter of ASKE, the Association for Skeptical Enquiry), December 2004.
Here's a quick puzzle that nicely fits into the 'logic and intuition' theme. I have found it useful for demonstration purposes in front of audiences. It is based on some research by psychologists in the US who have published their work in a learned journal but I read an account of it in one of my books on skepticism. I could try to locate the reference but it will probably take me umpteen hours, so forgive me if I leave this out on this occasion. Here is the puzzle.
Andy MacKay is a 24-year-old unmarried man who has a first-class honours degree in mechanical engineering. Whilst at University his motto was 'Work hard, play hard'. A keen sportsman, he nevertheless managed to enjoy an active social life, frequenting the local nightclubs and being 'popular with the ladies'.
The following are three statements about Andy McKay as he is now:
1. Andy McKay is a cashier at a Tesco supermarket.
2. Andy MacKay is a bank clerk.
3. Andy McKay is a bank clerk and is captain of the bank's rugby team.
The question is 'Which one of these statements is the most likely to be correct?' That is, if you were to place a bet, which would you put your money on?
The answer is given below, so do not look until you are ready.
The answer is we do not know. However, we do know that it is definitely not statement number 3.
The reason is that the number of men who are bank clerks is more than the number of men who are bank clerks and who are also captains of their firm's rugby teams. (There is just the remotest possibility that in reality all men fitting Andy MacKay's description who are bank clerks are also captains of their bank's rugby teams, in which case statements 2 and 3 are equally likely.) We can't decide between statements 1 and 3 without further information on the number of male members of these professions who fit Andy MacKay's description.
If everyone thought logically then no one would choose statement 3, yet a significant proportion does so - about 33% in my limited experience. (If you were asking an audience for their opinion you could see what happens when you announce that statement 1 is untrue and see what happens when those who initially chose this are allowed a second choice.) Why people do this may be because from the description of Andy MacKay it seems intuitively unlikely that he would be working either as a supermarket cashier or as a bank clerk. However, it does seem just like Andy McKay to be captaining a rugby team. Hence statement 3 seems to be the most fitting description. We may be tempted to overlook the fact, however, that neither of the other two statements implies that our hero does not captain a rugby team.
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