When reading this post (which is in my opinion one of the best posts on MSE by far), I read that the writing of Hamlet is a tail event, thus by Kolmogorov's zero-one law, it has a probability of either $0$ or $1$. However, generally when using Kolmogorov it is undecidable which of those is true. Are there examples where one can conclude by Kolmogorov that the probability of an event is $0$ or $1$ but also determine which of those is the right one?

  • $\begingroup$ What do you mean "it's undecidable"? That thread shows that it's $1$ and not $0$. $\endgroup$ – A.S. Dec 28 '15 at 22:35
  • $\begingroup$ Sorry, I'll edit the question. I meant that generally. @A.S. $\endgroup$ – implicati0n Dec 28 '15 at 22:36
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    $\begingroup$ Your edit changes nothing. The tail event of "produce infinitely many Hamlets" is either $0$ or $1$ and we can further restrict it to $1$. Are you asking about the opposite - when we cannot decide whether it's $0$ or $1$? $\endgroup$ – A.S. Dec 28 '15 at 22:41
  • $\begingroup$ You're not listening... I don't care about that post in my question. I wish to know this: I use Kolmogorov's zero-one law to conclude that an event (some event, not the writing of Hamlet) is of probability $0$ or $1$. After that, is there a way to decide which of those two is correct? @A.S. $\endgroup$ – implicati0n Dec 28 '15 at 22:48
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    $\begingroup$ Dude, you ain't expressing yourself well. You already have an example when you can decide which one it is. So is your question about general decidability of whether $P(A)=a$? Then it has little to do with Kolmogorov's law. $\endgroup$ – A.S. Dec 28 '15 at 23:03

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