How to prove independence from a word question

Question

Question: "You are recruiting students to participate in a study about alcohol consumption. Among all students, 30% have attend drunk, one-fifth of whom (i.e. 6% overall) are still drinking. To meet the quota for your study, you select students at random until you have found 20 still drunk. Let X be the number of sober students that you find before stopping. Let Y be the number of drunk students still drinking. Determine whether X and Y are independent. Explain your reasoning."

I'm not quite sure what explain means, but from past experiences, they usually want you to prove via theorems and what not.

Thanks

Answer 1

HINT:

You need to show $P(X|Y)=P(X)$. We can model X as a negative binomial random variable where we will stop after 20 "failures" to find a dunk person.

If there are $N\gg 20$ students in the population, then the failure probability is $p \approx 1-\frac{Y}{B}$

Since $Y$ determines the distribution of $X$ you'd expect these to variables to be correlated, and hence not independent.