(22-10-2023, 03:43 PM)MarcoP wrote: You are not allowed to view links. Register or Login to view.daily-random wrote:• 10 NUMBERS FROM 1 TO 500:
133 499 165 144 207 215 491 361 336 400
By the way, your example with numbers is perfect to demonstrate what I'm talking about. Imagine, that we have a number from 1 to 500, let's take the first number in your sequence: 133. What is the probability that another number starting with 13 will appear among the other 9 numbers? There are 11 numbers between 1 and 500 that start with 13 (13, 130-139), and there are 9 independently generated numbers, so the probability is 1 - (1 - 13 / 500) ** 9, or 21%. If another number starting with 13 appeared in this sequence, I'd call this curious, but not very remarkable.
On the other hand, the probability of finding two numbers sharing the same 2-digit prefix in this list is very high, I won't compute it here, but we can try adapting the Birthday paradox formula for this if needed. Edge cases like prefixes above 49, etc make it a bit complicated, but I won't be surprised if it's actually above 50%. And as you can see, 499 and 491 in your list share a two-digit prefix.
The probabilities of the co-occurrence of three prefixes from 72r3 and 67r2, given we chose labels on 67r2 before starting the experiment, is 0.58%. It's the same as the probability of any chosen number between 1 and 500 to appear among the first 4 numbers of the random sequence.
So, imagine you fix a number between 1 and 500 in your head, say 432 and generate 4 random numbers as above, and on the first try they go:
113 499 432 369
That's the level of statistical significance we are talking about. Not bullet-proof, and as I write in my text, particle physicists would laugh at this, but for the purposes of identifying meaningful patterns in the Voynich manuscript I find this more than enough.


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