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
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
- [JEE MAIN 2020]
- A
$\frac{31}{61}$
- B
$\frac{5}{6}$
- C
$\frac{5}{31}$
- D
$\frac{30}{61}$
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