Hi!

Say you have two distinct sets A and B such that A contains a non-zero finite number of elements and B contains an infinite number of elements.

You let C be the union of these A and B.

You pick an element X at random from C. (Same probability to pick any element.)

Questions:

1: What is the probability of X belonging to A?

2: Is it possible that X belongs to A?

3: Prove that it's possible/impossible that X belongs to A.

"Possible" might not be very well defined, please redefine "possible" in a suitable mathematical way if you see fit. Is perhaps possibly the same as having a non-zero probability or can something with a probability of zero occur? Am I mixing apples with lemons here?