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Thread: same birthday?

  1. #1 same birthday? 
    Forum Freshman
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    Hi everybody,
    the other day I was watching a programme on the BBC, and someone said you only need to collect 23 people at random to have 50% chances that at least 2 of them have the same birthday.

    So I set about calculating this probability for a generic N (number of people), and found this formula (leap year not considered):



    It seems to work, and it predicts 99.9% chances of at least 2 matching birthdays with as little as 70 people, and certainty (1) for N>=366.

    However, as the corresponding plot looks sigmoidal, my question is whether there is a nicer formula, where there is no index i.

    Thanks
    L


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  3. #2  
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    You can replace the product with a ratio of factorals, divided by a power of 365. However, the factorals are just disguised versions of products.


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  4. #3  
    Forum Radioactive Isotope MagiMaster's Avatar
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    There was another thread on this just the other day (http://www.thescienceforum.com/Perce...ity-27015t.php) though the question brought up was different.

    In that thread, we ended up working out a pretty good approximation to the final probability: . That always underestimates the actual probability by a little bit (past two people anyway).
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  5. #4  
    Veracity Vigilante inow's Avatar
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    Here's a video which makes it pretty simple to understand...

    http://www.youtube.com/watch?v=98OTsYfTt-c


    Note: It's in context of battling back religiot and spiritual claims, but the opening makes the concept being asked about in the OP quite clear.
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  6. #5  
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    Thank you for your answers. I like the approximated formula.
    And I didn't know Wikipedia had an entry for it.
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  7. #6  
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    For medium size n (365 >> n >> 0), you could use Stirling's formula to approximate factorals.
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