Damn, I wanted to edit so much that the timer ran out, lol
And this concept of leveraging probabilities for security is a great example how no system is [100%] secure.
We just need to make them secure enough. So secure that it's more way more likely that the sun is going to explode before you guess the correct random number. someone guesses your private key.1
Footnotes
There is more to it (like the security of a system needs to scale better than the resources of an attacker to be future-proof) but I'll leave it at that. ↩
Footnotes