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Math Help - Repeating an event probability Q.

  1. #1
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    Repeating an event probability Q.

    Hi there.

    Imagine I am playing a quiz machine which has a database of only 50 questions.

    How many questions would I have to answer on average before I get a repeat.
    (I guess I want the modal average?)

    Also a rough guide of how to think about this would be great!

    Thanks in advance of any replies.

    kop442000.
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  2. #2
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    ok I have made myself a little excel spreadsheet which I think is right... and now I can see the probability of a repeat after n number of questions.

    I make it that when you have seen 9 questions, you have 0.53 probability of having seen it before. Does this sound right?

    If so how do I convert this into the number of questions would I have to answer on average before I get a repeat?

    Is it just the number at which the probability hits 0.5?

    Thanks,
    Kop442000.
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  3. #3
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    ok I think I have it now.

    I calculate that I should expect to see a repeat after 9.54 questions. Feel free to correct or validate.

    Thanks.
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  4. #4
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    Quote Originally Posted by kop442000 View Post
    ok I think I have it now.
    I calculate that I should expect to see a repeat after 9.54 questions.
    That is exactly what I got using \sum\limits_{j = 1}^{50} {\frac{{P(50,j - 1)(j - 1)}}{{50^j }}j}  = {\text{9}}{\text{.54312703934395}}.

    I was hoping to find the general expectation formula.
    Maybe someone else recognizes this.
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