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I am curious about how other people think (model) probability questions?

Here is a sample question:

Suppose that each of N men at a party throws his hat into the center of the room. The hats are first mixed up, and then each man randomly selects a hat. What is the probability that none of the men selects his own hat?

  1. What is your first thought when you see this problem?
  2. Do you see images in your head? If so, what kind of images show up in your head? Are there images of hats in a bag for example?
  3. How do you model the problem?
  4. Why do you choose your model?
  5. What's your answer?
  • 4
    I'm not convinced that this question is a good fit for math.SE, but I don't want to take unilateral action, so I'll wait and see what others think. This is more of a psychology question than a math question.2012-05-18
  • 1
    Is this a homework question?2012-05-18
  • 1
    I find this question troubling, however, there is a possibility of a misunderstanding. Would you care to clarify what is the origin and the aim of this question? Also, what you want to learn from the answers and how are you going to use them? This looks to me exactly like someone doing psychology experiment (or something similar) and judging from your previous questions this is not far fetched.2012-05-18
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    I also vote to close this question as "off topic", but I will wait to see what others think since my vote is binding.2012-05-18
  • 0
    it's not for a psychology experiment or anything of that sort. it's for my own education purposes. probability questions lend itself to being solved in many ways with different models. i think of generating sequences; my friend thinks "fractions"; some people try to relate to "toss a coin" or "flip a die" or "bag" models. i feel it's really important how you start a probability problem. i wanted to see the different approaches to solving the problem.2012-05-19
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    Ok, this did convinced me enough to answer your question (so you won't leave empty-handed), but I still think it's not a good fit for math.SE. For your convenience: 1. Permutation. 2. Yes, bipartite graphs, no. 3. $|\Omega|=|S_n|$. 4. It is exactly the abstract formulation of the problem. 5. This is a well-known problem, with $\lim_{n\to\infty} P(A) = e^{-1}$ as stated by Somabha Mukherjee below.2012-05-19

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