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Homework Help: Mathematical Probability Question

  1. Feb 12, 2010 #1
    I spent quite a lot of time trying to figure out this question that I read in a book. Through trial and error, I got a rough idea of what the solution should be like but can't figure out how I would derive it mathematically. Can anyone give me some directions? :)

    QUESTION:

    n people stand in a circle, where n > 2. we pick two person, A and B, at random. what is the probability that there are exactly r people standing in between A and B, in the clockwise direction?
     
  2. jcsd
  3. Feb 12, 2010 #2

    tiny-tim

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    Hi Legendre! :wink:

    Can you think of a way of simplifying the question? :smile:
     
  4. Feb 12, 2010 #3
    Given a choice of A, how many B's will satisfy the condition?
     
  5. Feb 12, 2010 #4

    tiny-tim

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    Yup! :biggrin:

    (or, rather, what proportion of B's will satisfy the condition?)

    So you can simplify the problem by arbitrarily fixing A, which makes the answer … ? :smile:
     
  6. Feb 12, 2010 #5

    Redbelly98

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    Moderator's note: thread moved to Homework forums.
     
  7. Feb 15, 2010 #6

    Thanks for not outright giving the answer! I find that I learn much more if I were to come out with an answer using hints.

    Now lets see...

    Fix A. Counting in the clockwise direction, only 1 B satisfies "exactly r people are standing between A and B".

    0 <= r <= (n-2). So there are (n-1) possible r.

    So the probability is 1/(n-1).
     
  8. Feb 15, 2010 #7

    tiny-tim

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    (just got up :zzz: …)
    :biggrin: Woohoo! :biggrin:
     
  9. Feb 15, 2010 #8

    haha thanks!
     
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