Players A and B roll a pair of dice in turn, with player A rolling first. A's objective is to obtain a sum of 6 (on one roll), while B's ojective is to obtain a sum of 7. The winner is the first player to reach his or her objective. What's the probability that player A wins?
Does my approach make any sense? I'm probably making this way too hard.
I let be the event that A wins, and be the event that player A rolls a sum of i (i=2,3,...,12) on his first roll.
when , , which is the probability that player B does not win on his first roll times the probability that A wins (assuming independence of course)
and then solve for
I get 30/61, or about 49%