See figure attached below for the question.
I was struggling with part a).
Is there a systematic way of solving for the sample space in this question? (I'm having a hard time determining whether I've truly written down every permutation of winning)
The outcomes that only last 3 or 4 sets it is still fairly clear whether you've obtained all possible outcomes or not, but for the outcomes that require 5 sets I find myself racking my brain to determine whether or not I've actually listed all the possible outcomes.
Is there a way to systematically determine this? For example, if I knew from the beginning that there would be 20 samples in my sample space when I have listed say 18, I would know that I am still missing 2 possible samples.
The only way I could think of simplifying things when generating this sample space is to create a sample space that contains all the games where one particular player ones. Then for the total sample space I would simply invert all the entries so that all the games that the other player could have one are covered as well.