This sounds like a geometric with probability of success
I think I had my p's and q's backwards, I misread the NOT equal to zero.
And what's X doing here?
Consider independent trials each of which results in outcome i, i=1,2,...k with probability p of i. Let N denote the number of trials needed to obtain an outcome that is not equal zero and let X be that outcome. Find P(N=n) where n>=1
Thanks so much!