Abe and Bill are playing a fun game. Each of them roll a dice every turn. Abe succeeds if he rolls either a 1 or 2. Bill succeeds is he rolls either a 3, 4, or 5.
If they both succeed on a turn, then they tie the game. If exactly 1 player succeeds on a turn, then the succeeding player wins. If neither player succeeds on a turn, another turn occurs.
What's the probability that Abe will win? I originally thought that the answer was $\frac{2}{5}$, but I realized that the players could tie as well.