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Stan is a young man. He:

  • is shy
  • is neat/tidy
  • needs order
  • pays high attention to detail

Is Stan more likely to be a librarian or a farmer?

Answer:

Many people would say librarian despite several important considerations. Statistically speaking there are more farmers then there are librarians.

I don't understand this. No where does it mention statistics... I don't understand how there are supposedly these magical important considerations, unmentioned, that I just obviously should have taken into consideration. What makes this answer the way it is, and what type of thinking is this called so I can look it up and learn it.

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closed as off-topic by boboquack, Ankoganit, Alconja, JonMark Perry, Rubio Jun 15 '17 at 6:21

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  • $\begingroup$ I think that this question might invite speculative answers, as the question isn't fully defined. Is there a definite answer to this, relevant to puzzles, or is this just a matter of personal opinion? $\endgroup$ – boboquack Jun 15 '17 at 1:25
  • $\begingroup$ From what I understand, the "correct" answer is that Stan is more likely a farmer, because statistically speaking, there are more farmers than librarians in the world. $\endgroup$ – Michael Cermak Jun 15 '17 at 1:32
  • $\begingroup$ Welcome to Puzzling! (Take the Tour!) Your question is, essentially, "why am I expected to take into account these unmentioned magical important considerations to solve this puzzle?" - and the answer may very well be, "Because the puzzle is bad." Making a logical leap is often the most satisfying part of solving a puzzle. Being expected to make an unobvious, completely unmotivated step to solve a puzzle is, as you've found, frustrating. Having said all this--your question here probably is unanswerable, or at least may have no single best answer. $\endgroup$ – Rubio Jun 15 '17 at 1:32
  • $\begingroup$ Ok, so I was most likely right in thinking it was an absurd question. All I know is that when I heard it, it sounded extremely illogical as though it was a question written by an egotist who just wanted to confuse the listeners, and sound intellegent by having an answer. Though I suppose too since it says "Is stan more likely" likely being the key word, I guess you could then look at statistics. Still think that a really long stretch though... $\endgroup$ – Michael Cermak Jun 15 '17 at 1:40
  • $\begingroup$ To illustrate Gareth McCaughan’s answer, consider this variation: “I have a cat named Emerald. Is the cat more likely to be gray or green?”  The answer is “gray”, because gray cats are much more common than green cats (statistically). You should not be misled by the fact that the cat’s name is the name of a green gemstone. $\endgroup$ – Peregrine Rook Jun 15 '17 at 4:06
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I'm pretty sure I know what's going on here. The question really isn't a puzzle in the sense that's usual here. Rather, it's trying to make a point that's actually applicable in the real world.

When you're asked a question of the form "Here's some information. Now, what's most likely?" two things ought to feed into your answer: (1) what the chances were before you learned the specific information and (2) the impact of that specific information. The first is sometimes called the prior or the base rate.

And it turns out that people very commonly -- not just when answering artificial questions like this one, but in everyday life as well -- forget to take #1 into account because #2 is so much more prominent. This is sometimes called "base rate neglect".

Here's a not-so-artificial example. Suppose you get tested for a Very Rare Disease, and the test comes back positive. It's a pretty reliable test: it only produces false positives 10% of the time. Does that mean there's a 90% chance you have the disease? No! Remember that the disease is very rare. It may well be that even after a positive test result you are much more likely not to have it. (Note: the odds may be different if you are having the test because there are other reasons to suspect you have the disease.)

So, the point of this question -- at least originally, who knows how it may have been being used when you encountered it? -- is to let you discover how seductive base rate neglect is, and then point out that base rate error is a mistake. So you see all those character traits that are somewhat typical of librarians, think "aha, the person is probably a librarian", and then get hit with the observation that actually they're more likely to be a farmer.

Now: is it an absurd question, as the OP suggests in comments? Maybe. Librarians are less common than farmers, indeed. But if you, like (I suspect) many people here, are a middle-class city-dwelling intellectual, then your situation may be like that of the person who gets tested for a rare disease because there's already reason to suspect they have it. There are a lot more farmers than librarians, but you may well be more likely to meet a librarian than a farmer. If you or I meet someone with all those character traits, I suspect they are more likely librarian than farmer.

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  • $\begingroup$ Not sure I get it, if you get tested positive and it is not a false positive, how is it that you might not have the disease? $\endgroup$ – stack reader Jun 15 '17 at 6:53
  • $\begingroup$ @stackreader Lets say there is 1:1000 chance to have disease and 1:10 chance that test will show the positive no matter what (or opposite). So if you got positive test, there is still only 1% chance that you have disease. $\endgroup$ – Jan Ivan Jun 15 '17 at 7:04
  • $\begingroup$ @stackreader If it's not a false positive then you have the disease, by definition. But although false positives are rare, they may be much rarer than people who actually have the disease, and therefore a positive result may be more likely a false positive. $\endgroup$ – Gareth McCaughan Jun 15 '17 at 10:15
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    $\begingroup$ Imagine a disease that afflicts 1/10000 people and a test that gets the right result 99/100 of the time. We test 1000000 people; 100 of them have the disease; one is reported not to and the other 99 are reported as having it. Of the other 999900 people, the test correctly says that 99*999900=98990100 don't have the disease, but identifies 9999 people as having it. So, we have 99+9999=10098 people with positive test results, but only 99 of them actually have the disease: about 99% of people with positive results don't have the disease. $\endgroup$ – Gareth McCaughan Jun 15 '17 at 10:19

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