Linked Questions
12 questions linked to/from Given an infinite number of monkeys and an infinite amount of time, would one of them write Hamlet?
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infinite monkey problem - probability of an infinite sequence containing an infinite sequence [duplicate]
Note: This question is specifically about when the infinite monkey theorem is extended to reproducing an infinite sequence (as oppose to a finite one)
I was browsing wikipedia, and came across the ...
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Proof of infinite monkey theorem. [duplicate]
I was just wondering, does the infinite monkey theorem also has a proof? And why is this called a theorem? It is sheer common sense. And what are its applications. I have heard about PHP and IEP and I ...
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Infinite Coins Tossed Infinitely Often [duplicate]
If an infinite number of coins are tossed infinitely often, is it true that there will be infinite subsets of those coins that repeat any finite sequence of heads/tails infinitely often? I.e., ...
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What is the probability for a monkey writing Shakespeare? [duplicate]
The article clearly describes the idea but does not the state the probability. What is the probability? Can this problem be extended to audio, graphics and video for instance what is the probability ...
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Monkeys and Typewriters
Suppose that there is a certain collected works of plays that is N symbols long in the following sense: a "symbol" is one of the 26 letters of the alphabet, a line break, period, space, or a colon; in ...
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Probability of Monkey typing keyboard
A monkey types at a 26-letter keyboard with one key corresponding to each of the lower-case English letters. Each keystroke is chosen independently and uniformly at random from the 26 possibilities. ...
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Would these 2 infinite sets be equal, if so why?
My friends and I were asking the following question:
If Minecraft worlds were to be infinite, does that mean that every Minecraft world is identical? My friends and I are adding this constraint to say ...
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What is the probability that an event happens an infinite amount of times in infinite trials?
For example, that in an infinite amount of coin flips, the event that the result are head k times in a row happens an infinite amount of times.
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A Monkey Choosing Real Numbers for an Infinite Time
A common illustration of the nature of infinity is that, given an infinite amount of time, a monkey on a typewriter will, with probability $1$, produce the complete works of Shakespeare.
Consider now ...
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Kolmogorov's zero-one law
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 ...
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Is this probability theorem correct?
Let me preface my question by saying that I am not a formally trained mathematician, so please forgive my informal statement of my problem.
I have the following 'theorem' of an idea that I believe to ...
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Nonuniform infinite random monkeys and Hamlet
I have a rudimentary grasp of the second Borel-Cantelli lemma and vaguely understand how finite patterns can repeat infinitely often. The one proof I am familiar with that verifies this unfortunately ...
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