As a student many years ago I learned of a paradox of something that is almost a certainty, while at the same time being highly improbable.
For example, if you flip 10 coins the chances of all being heads is very slim. However, if you have an entire Superdome full of people perform the experiment, someone will have an all-heads result.
I thought this paradox has a name but possibly I'm not remembering it correctly or I'm mistaken because I've been googling to no avail...
On
Just a quick clarification: What you're describing is not actually a paradox--rather it's a property of Probability.
So, for example, if you start flipping a coin over and over for the rest of eternity, the probability that you only get "heads" for each and every flip is infinitely small. However, you can't say that this outcome is impossible. Instead, the most we can say is that if we start flipping a coin we will almost surely get at least one "tails".
I believe you are referring to some version of the Infinite Monkey Theorem.