In a game two players $A$ and $B$ take turns in throwing a pair of fair dice starting with player $A$ and total of scores on the two dice, in each throw is noted. $A$ wins the game if he throws a total of 6 before $B$ throws a total of 7 and $B$ wins the game if he throws a total of 7 before $A$ throws a total of six. The game stops as soon as either of the players wins. The probability of $A$ winning the game is: (1) $\frac { 5 } { 31 }$ (2) $\frac { 31 } { 61 }$ (3) $\frac { 5 } { 6 }$ (4) $\frac { 30 } { 61 }$
In a game two players $A$ and $B$ take turns in throwing a pair of fair dice starting with player $A$ and total of scores on the two dice, in each throw is noted. $A$ wins the game if he throws a total of 6 before $B$ throws a total of 7 and $B$ wins the game if he throws a total of 7 before $A$ throws a total of six. The game stops as soon as either of the players wins. The probability of $A$ winning the game is:\\
(1) $\frac { 5 } { 31 }$\\
(2) $\frac { 31 } { 61 }$\\
(3) $\frac { 5 } { 6 }$\\
(4) $\frac { 30 } { 61 }$