JEE Main 2021 (Online) 4th August Morning ShiftQuestion 1
Two players $A$ and $B$ play a game. Player $A$ first throws a fair die and if $5$ or $6$ appears, he wins; otherwise player $B$ throws a fair coin and wins if head comes. The process continues till someone wins. The probability that $B$ wins after completion of $3$ or more throws of the die, is
Probability
Solution
Each round: A wins w.p. $\frac13$; else B wins w.p. $\frac23\cdot\frac12=\frac13$; game continues w.p. $\frac13$. B wins in round $k$ w.p. $(\frac13)^{k-1}\cdot\frac13=(\frac13)^k$. Required $=\sum_{k\ge3}(\frac13)^k=\frac{1/27}{1-1/3}=\frac1{18}$. Option A.