JEE Main 2023 (Online) 6th April Morning ShiftQuestion 1
A pair of dice is thrown $5$ times. For each throw, a total of $5$ is considered a success. If the probability of at least $4$ successes is $\frac{k}{3^{11}}$, then $k$ is equal to
Probability
Solution
$p=\frac4{36}=\frac19$. $P(\ge4)=\binom54(\frac19)^4\frac89+(\frac19)^5=\frac{40+1}{9^5}=\frac{41}{3^{10}}=\frac{123}{3^{11}}$. $k=123$. Option C.