# 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!