You roll a die until you have seen a 5 on 4 of the rolls (e.g. ⟨5,3,2,5,4,1,6,5,2,5⟩. What is the expected number of rolls this will take?
I think that I am way overthinking how I should be going about doing this. I know that I need to use a geometric distribution because I roll until I have seen 4 "fives". (I edited it.)
My attempt: 1/5 * (6^n+1) = 1554. That cannot be right. Anyone who can help push me in the right direction would be appreciated.