A friend and I have been trying to figure out this seemingly simple problem for a while and couldn't find any help with it anywhere online. The problem is as follows:
What are the odds of rolling a seven at least once (that is, once, twice OR three times) in three rolls of two dice?
The closet we could come up with is (1/6)+(1/12)+(1/18) which gives the logical looking number of 30.5%, but (we think) that assumes you stop rolling if you roll a seven. At this point I can't even tell if that matters.
(If you're wondering, the impetus for this question is the boardgame Settlers of Catan - I wanted to know, with three people playing, what the probability is of a 7 being rolled between the end of your turn and your next turn, i.e. 3 rolls)
Thanks a lot.