JEE Main 2023 (Online) 10th April Evening ShiftQuestion 1
Let a die be rolled $n$ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is $\frac{k}{2^{15}}$, then $k$ is equal to
Probability
Solution
$\binom n7=\binom n9\Rightarrow n=16$; $p=q=\frac12$. $P(\text{even twice})=\binom{16}2\frac1{2^{16}}=\frac{120}{2^{16}}=\frac{60}{2^{15}}$. $k=60$. Option C.