Like the infinite monkeys typing Shakespeare, but with audio instead.
If there was a program that created a series of sounds at random intervals, pitches, amplitudes, etc., how long would it take to produce an output that sounds like music, some sort of recognisable recording (e.g. a bell ring, a dog barking), or perhaps even a human voice?
If it is truly random, where every outcome is equally likely, then Beethoven’s 5th could be the first thing produced. It could also take an infinite amount of time to produce.
If every outcome is equally likely, then the probably of any given outcome is approaching one in infinity…
Yes, that’s right. Which means that any specific outcome is essentially impossible to occur. But given infinite time, they all would occur.
Not necessarily. Roll a twenty-sided die twenty times, and you’re not guaranteed to roll every number.
Roll an infinite-sided die infinity times, and there’s no guarantee either.