A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a sum of 8 before A…

$\displaystyle A$ and $\displaystyle B$ alternately throw a pair of dice. A wins if he throws a sum of $\displaystyle 5$ before $\displaystyle B$ throws a sum of $\displaystyle 8$ , and $\displaystyle B$ wins if he throws a sum of $\displaystyle 8$ before $\displaystyle A$ throws a sum of $\displaystyle 5$ . The probability, that $\displaystyle A$ wins if A makes the first throw, is