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Math Help - Probability of at 1 matching pair

  1. #1
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    Exclamation Probability of at 1 matching pair

    This problem is found in the chapter titled "Union, Intersection, and Comlement of Events; Odds" in my textbook Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences. I have been looking at it for quite a while now and the book gives no decent examples as far as I'm concerned. Here is the problem:

    In a group of n people (n <= 100), each person is asked to select a number between 1 and 100, write the number on a slip of paper, and place the slip in a hat. What is the probability that at least 2 of the slips in the hat have the same number written on them?

    I just don't have any clue on how to tackle this. If it weren't an even-numbered question then I'd be able to look for the answer in the back of the book and get an idea of what the output should be, but that isn't the case.

    EDIT: I just realized that I may have put this in the wrong section. This is a university finite mathematics course, but it seems as though the rest of the posts in here are much more advanced. My apologies if I was in the wrong to put this here.
    Last edited by mr fantastic; April 13th 2010 at 07:59 PM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by timzim View Post
    This problem is found in the chapter titled "Union, Intersection, and Comlement of Events; Odds" in my textbook Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences. I have been looking at it for quite a while now and the book gives no decent examples as far as I'm concerned. Here is the problem:

    In a group of n people (n <= 100), each person is asked to select a number between 1 and 100, write the number on a slip of paper, and place the slip in a hat. What is the probability that at least 2 of the slips in the hat have the same number written on them?

    I just don't have any clue on how to tackle this. If it weren't an even-numbered question then I'd be able to look for the answer in the back of the book and get an idea of what the output should be, but that isn't the case.

    EDIT: I just realized that I may have put this in the wrong section. This is a university finite mathematics course, but it seems as though the rest of the posts in here are much more advanced. My apologies if I was in the wrong to put this here.
    The approach is similar to that used in the Birthday Paradox (Google it).
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    The approach is similar to that used in the Birthday Paradox (Google it).
    Thank you very much for pointing me in that direction, it was exactly what I needed to see.
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