Is the mathematician's world really so insular,that someone from outside asking some questions about how a problem relates to concepts he understands gets downvoted?
Or are you pretending that unless you skate with ease over three different kinds of infinities, their differences and similarities, and the paradoxical results of probability problems with infinity in the numerator and denominator, that you are just a time wasting intruder on an otherwise valuable conversation?
Or did my questions, which I'd love to know the answer to, come across as a veiled negative comment?
Your questions were easily answered by looking up the definitions of the terms "finitely many" and "countably infinite".
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.