JEE Main 2020 (Online) 4th September Evening ShiftQuestion 1
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 :
Probability
Solution
$P(A\text{ throws }6)=\frac5{36}$, $P(B\text{ throws }7)=\frac16$. $P(A\text{ wins})=\frac{5/36}{1-\frac{31}{36}\cdot\frac56}=\frac{5/36}{61/216}=\frac{30}{61}$. Option D.