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Recently I read about how many people it takes for the probability that two or more share the same birthday to be sufficiently high.

My question: How many people do I have to know that I could be sufficiently sure (>95%) that I have to congratulate at least one person every day for the whole year, that is, all 365 days?

kjetil b halvorsen
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Taufi
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    This is a version of the Coupon Collector problem, not the Birthday problem. – whuber Mar 31 '16 at 19:32
  • Thanks, I was not aware the problem already existed. – Taufi Mar 31 '16 at 19:33
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    I provide a full analysis of this distribution for a generalization of the problem at http://stats.stackexchange.com/a/202393/919 . At the end I also give an approximation to the value you seek (use $p=1$ in your case). That approximation gives 3247 people. It should be pretty accurate. The R program mean(replicate(1e4, 365==length(union(integer(0), floor(runif(3247)*365))))) simulates 10,000 instances of this situation (within a few seconds) and consistently produces answers close to 95%. – whuber Mar 31 '16 at 19:35

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