probability – What is the issue with random variable Z?

When opening a container of $32$ toy ballet dancers performing pirouettes, let random variable $X$ denote the number of broken dancers,
and let random variable $Y$ denote the number of whole (unbroken) dancers.
Write random variable $Z = X/Y$ , i.e., $Z$ is the ratio of broken dancers to whole dancers.
What complication arises in this definition of $Z$ as a random variable?

So my work: X and Y are clearly discrete random variables with $X in {0,1,2,…,32}$ and $Y in {0,1,2,…,32} $

But wouldn’t $Z$ be just another discrete random variable? with $Z in {0, 1/31, 2/30,…, 1}$?

With no issue?

My question is What’s the Issue with $Z$? I’m not seeing it. Can someone help me see the issue?

Thank You!