Each of 1000 balls is thrown and lands randomly into one of 1000 pots. What is the probability that at least one pot will have 34 or more balls?
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$\begingroup$ What have you tried? $\endgroup$– David G. StorkCommented Feb 20, 2022 at 22:05
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$\begingroup$ See this generic duplicate, ignore the first answer as it is wrong. The second answer is conceptually useful but, as it mentions, the computations are so unwieldy that people tend to either simulate the thing or fall back on asymptotic analysis. $\endgroup$– luluCommented Feb 20, 2022 at 22:06
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$\begingroup$ @lulu - given there are three answers there (currently two with the same numbers of votes) it might be worth identifying which one you are pointing at $\endgroup$– HenryCommented Feb 20, 2022 at 22:16
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$\begingroup$ @Henry Thanks for pointing that out. I meant the answer from Ian. The incorrect one is the one from Mostafa Ayaz. And the links provided in the comments might be helpful as well. $\endgroup$– luluCommented Feb 20, 2022 at 22:17
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$\begingroup$ The answer is going to be very small in your case: you can work out the probability the first pot has $34$ or more, and thus the expected number of pots with $34$ or more. That will be an upper bound on the probability any are (and in this case, very close to the probability) $\endgroup$– HenryCommented Feb 20, 2022 at 22:26
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