geometric distribution throwing a die
Yesterday I posted a question which was answered but I disagree with the answer so I'd like to ask again so we can discuss it together :)
The problem says as follows: We throw a die repeatedly. X and Y denote, respectively, the number of rolls until we reach a 5 and 6 . The aim is to compute $E[X|Y=5]$.
First question: If Y=5 (this means no 6 have come up in the first 4 rolls) then the probability of getting 5 in those rolls should be 1/5 instead of 1/6?
I have done some simulations to guess the expected number of rolls and I get always something around 5.8 which seems reasonable but I can't arrive to that answer algebraically or analitically.
Thanks a lot for you help! :)