I was linked a youtube video where the first two characters were underscores, how could I calculate the probability of that happening? 64 possible characters, 11 character long string, and only two underscores appearing twice at the beginning. Is this possible?
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3$\begingroup$ Probability under what distribution? It’d be impossible in a language that doesn't use it, and quite likely if it's a Morse code written using “.” and “_”. $\endgroup$– TimCommented Mar 1, 2023 at 7:30
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1 Answer
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If you assume that all characters are equally likely to appear at any position (not likely for any "real" language, but probably a reasonable assumption for auto-generated URLs), then the probability for an underscore at any particular position is $\frac{1}{64}$.
If you also assume that characters are independent (again see above), then the probability for two underscores is $\frac{1}{64}\times\frac{1}{64}\approx 0.0002$.
answered Mar 1, 2023 at 7:37
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$\begingroup$ This assumption alone does not determine your answer. You are implicitly assuming the characters are drawn independently. For a common application where the characters meet your initial assumption but are not independent, see any of our threads about Scrabble. $\endgroup$– whuber ♦Commented Mar 1, 2023 at 15:49
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$\begingroup$ @whuber: I write in my second paragraph that if we can assume independence, the result follows. Where is my error? $\endgroup$ Commented Mar 1, 2023 at 16:06
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$\begingroup$ Sorry -- I was looking for assumptions at the outset and overlooked your clearly stated assumption in the second paragraph! +1. $\endgroup$– whuber ♦Commented Mar 1, 2023 at 17:18