This involves some quite technical mathematics.
Let's take an example. How would you go about counting all the real numbers between 0 and 1 without missing any of them out? I will tell you now that you can't do it. The reason you can't do it is because the set of all real numbers between 0 and 1 is an uncountably infinite set.
Of course, you could doubtless devise some scheme for counting some of them, but, even if you had an infinite amount of time available, you would never count all of them. In fact, you would be doomed to miss most of them out. Therefore, the chances of you naming any given real number, chosen at random by somebody else, would be vanishingly small.
The set of all rational numbers is a countably infinite set, so you could count all of them, if you had an infinite amount of time, but you couldn't count all the reals between 0-1, even with an infinite amount of time available to you.
You're wrong. And I can tell you the probability of hitting any specific number randomly if I were given an infinite amount of time. Lets say 4.7658624639754173047463930262538464838.
The probability of hitting that number is
infinite (number of possible outcomes)
divided by
infinite (number of attempts)
Equals
1 or 100%
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