First of all, i am only a newbie and i am pretty sure that my thinking is faulty somewhere, so along the way as i explain things i will probably say something with an error and i hope you will help me find this error. This idea has been bogging me for some time already.
Imagine picking a random real number. Without the loss of generality, let the picking interval be $(0,1)$, or $<0,1>$.
Now, since there is an infinite amount of real numbers, the probability of choosing one specific number is $0$.
Yet, we have to pick one number when choosing randomly, let's say it's $0.5$. We have now picked a number that had $0$ chance to be picked.
How is this possible?
Thank you for all the answers, i have had hard time deciding what to pick as "correct" answer as i came seeking answers.
EDIT: Recently, i saw these Binomial Distributions video series and this video explains it pretty well