How to find out the conditional expectance

Question

Let $X$ be a random variable with $X\sim\mathrm{Geom}(1/3)$. Let $Y$ be another random variable with $Y\sim\mathrm{Bin}(n, 1/4)$ where $n$ is the value taken by the random variable X.

I'm trying to find $ E(Y|X=n)$. I know the formula and how to do it if I were given a set of values but how do you tackle the unknown variable?

Answer 1

I think you said it earlier. If you have n draws with 1/4 chance success, you expect n/4 successes total. The geometric part does not come into play because we essentially come in after finding out $X=n$ for some value $n$ we don’t specify yet.