this post was submitted on 23 Jan 2024
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Showerthoughts

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[โ€“] xigoi@lemmy.sdf.org 11 points 11 months ago

Then there is every second a nonzero chance that this machine (assuming true and not pseudo randomness) will pick, say pi.

No. The probability of picking any particular number from a uniform distribution is 0.

On the contrary, since the works of Shakespeare are a finite string over a finite alphabet (I can formalize this argument if you want), the probability of typing them out after some fixed large number of keystrokes is some nonzero number ๐‘. With ๐‘› monkeys, the probability that at least one will type out the works is 1 โˆ’ (1 โˆ’ ๐‘)โฟ, which goes to 1 as ๐‘› โ†’ โˆž.

Now, you are right that this does not mean that the works are guaranteed to be typed out. However, it has probability 1, so itโ€™s mathematically โ€œalmost certainโ€.