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Does the birthday problem change if we only take people from the same year (e.g. a classroom)?

Intuitively I think it does, because you have more probabilities to have two people born in different years on the same day and month than to have them on the exactly same date. But with only intuition and no demonstration, this is a weak argument.

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    $\begingroup$ Count for what? Please tell us what kind of problem you are dealing with. $\endgroup$ May 29, 2015 at 11:53
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    $\begingroup$ I don't think it matters, as long as the probability of being born on a specific date does not change over time. $\endgroup$
    – George
    May 29, 2015 at 12:52
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    $\begingroup$ The birthday problem just refers to day of year. $\endgroup$
    – Nick Cox
    May 29, 2015 at 14:00

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It actually does not. The birthday "problem" as usually stated (there's actually no problem...) only relies on days of the year (and an independence assumption).

Most of the time intuition in statistics must be double-checked by calculation, in here the calculation (no matter how you do it), does not use the year, hence the problem is independent from the year.

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