@bunyip, once the monkey generates the first word or page, the probability that the next letter will match the next word of Shakespeare's sonnet will always be 1/26. What's your point? This is all well known.
The correct answer to this topic is 1, for the rest go talk with the stupid Elubas in chess.com.
@acgusta2, I already wrote (on the first page of this topic) that number of integers is insufficient. @lecctra, one person will generate 1/3 with probability 0, which isn't particularly helpful.
@lecctra
you obviously are are a gambler.please google "the gambler's myth".
That will explain to you why casinos always win..and gamblers never win in the long run.
@Otienimous And infinite people will generate probability: infinity x zero which is undetermined., So what's your point again?
1 person is enough even with 0 probability, for the rest like I've told you before go talk with Elubas at chess.com, or with @bunyip
@lecctra, infinity*zero sometimes may be determined. To be more precise: if we have two sequences, sequence a with limes 0 and sequence b with infinite limes, sequence a*b may have limes 0, infinity, something in between or no limes at all. Basic calculus. In this particular case you can have one person for every natural number and there is still zero chance that one of them will generate 1/3. Proving this fact is mildly untrivial and really funny.
@bunyip, I doubt whether the gambler's fallacy has much to do with this topic. It is obvious, hereby, that in every consecutive dice roll digit 3 has one chance in ten.
@Otienimous The possibility 0 is still a possibility like 0 is still a number although it indicates nothing. So in your question one person suffices to generate (1/p)^n as n tends to infinity. End of the long story.
@lecctra , by "generate 1/3" I of course mean, as per original post, rolling an infinite series of 3 by one's dice (or, equivalently, choosing a random real number from <0, 1> and getting 1/3). It is actually fascinating that you can have infinitely many people (one for every natural number) and there is still zero chance that one of them will roll it. Your "end of the long story" looks like a classic case of diminishing something incomprehensible.
@acgusta2 That would be a countable infinity (the smallest one), since the rationals (of which 1/3 is a member) are a countably infinite set.
For the curious: https://en.wikipedia.org/wiki/Countable_set
@Genetic_Chess_Bot No, it wouldn't be. 1/3 is indeed rational, but it is also real. In the riddle, a random real number is taken from <0, 1>, not a random rational number. And reals are uncountable.
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