Consider the following premise:
There are a (countably, obviously) infinite number of monkeys, each with a typewriter, and each equipped to type for an infinite amount of time.
Given this premise, assume the following:
The first monkey types “$kpkpkp...$”, repeating this sequence infinitely.
The second monkey types “$kkpkkp...$”, repeating this sequence infinitely.
The third monkey types “$kkkpkkkp...$”, repeating this sequence infinitely.
...
The $n^{th}$ monkey types “$kk...kpkkk...p...$”, repeating a sequence of $n$ $k$’s and then a $p$ ad infinitum.
Now, it’s true that I have dictated what each monkey will type, but even so, ask yourself the following:
1.) Is this an infinite number of monkeys typing for an infinite amount of time?
2.) However unlikely this particular scenario may seem, is it a $POSSIBLE$ outcome of the given premise?
3.) Is each monkey’s “manuscript” unique?
4.) Will any of these monkeys ever type $Hamlet$? Or $Speed$ $2$? Or even an existing English word? (If so, which monkey will be the one, since we already know what each will put forth?)
The answers are quite obviously “yes” to the first three questions, and “no” to the last.
Again, although I’ve dictated a very specific prescription that this set of monkeys must stick to, this is still a counterexample (this is not a question of probability!). That is, nothing guarantees that this scenario won’t happen.
Hence, the reproduction of $Hamlet$ is not guaranteed.