An ubiased die is successively rolled. Let X and Y denote, respectively, the number of rolls necessary to obtain a six or a five. Find (a) E[X], (b) E[X|Y=1], (c) E[X|Y=5]

This problem is giving me fits. At first I thought that the events were independent, but now I don't believe they are.

(A) X~geo(p=1/6) So, E[X]= \frac{1}{\frac{1}{6}}=6

Or is it \frac{1+2+3+4+5+6}{6}=\frac{21}{6}?

(B) The book just has \sum_{x}xp_{X|Y}(x|y)] so I'm trying to figure a way to get it into that format.

(C) Same as (B)

Im going to keep working at this, but any suggestions would be helpful. Thsnks