Say we have a fair six-sided die, and we want to find the expected number of 1s rolled before the first six is rolled.
Apparently this can be solved by conditioning/recursion. I know that by that same method there are 5 expected rolls before rolling a 6 (with roll 6 being 6). Thus the expected number of 1s before that should be much less than 6.
Would I rewrite this problem to the expected number of 1s rolled in $6-1=5$ rolls (the rolls before the first six)? I'm not sure how to start solving this.