You are trying to locate an old high school friend who lives in Chicago. Unfortunately, your friend's name is Anthony Smith and the Chicago phone book lists phone numbers for $24$ different people named Anthony Smith. (Assume that your friend's phone number is listed in the phone book, and that you don't call anybody twice.)
Let $X$ be the number of calls you need to make until you find your friend. Give the probability mass function for $X$.
I think $X$ will have a Geometric distribution? but with what $p$?? Also, as I know in the geometric distribution the number of trials could be infinity, but here we have at most $24$?