I have 26 tiles each one with a different letter of the English alphabet: $A, B, C,...,Z.$
I draw two tiles with replacement. The possible outcomes are: $$S=\{AA, AB, AC,..., AZ, BA,...,ZZ\},$$ which contains $26^2=626$ elements.
Now define the random variable $X$ which counts the number of vowels I draw. X can take on 3 values: 0, 1, or 2. Let U={0,1,2} which is the set of possible values that X can take. I am describing is an elementary example of the Binomial distribution.
What I need help with is knowing the correct name for the set S, and the set U described above.
Is it outcome space, sample space, event space?
I know outcomes are things that can happen in an experiment like rolling a six-sided die the outcomes are S={1,2,3,4,5,6} but an event is some subset of the "set of all sets". For example the event might be rolling a prime number for which there are three possible values U={2, 3, 5}
What is S in both examples called? What is U?
Thanks.