This is one of the past questions from the entrance exam for the graduate school.
I think I know the answer but I would welcome help with the authoritative answer.
Each time a coin is flipped, it has probability p of a HEAD and q of a TAIL. Let random variable X denote the number of flips until the first HEAD.
(i) Show that P(X>1) = q.
(ii) Write an expression for the conditional probability mass function P(X=x|X>1) in terms of p and q.