JEE Main 2025 (Online) 24th January Morning ShiftQuestion 1
$A$ 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 $A$ throws a sum of $5$. The probability, that $A$ wins if $A$ makes the first throw, is
Probability
Solution
$P(5)=\frac19$, $P(8)=\frac5{36}$. $P(A\text{ wins})=\frac{1/9}{1-\frac89\cdot\frac{31}{36}}=\frac{36}{76}=\frac9{19}$.