Question:

A fair $n$-faced die is rolled until a number $<n$ appears. If mean of tosses $=\dfrac{n}{9}$, then $n$ is equal to

Step-by-Step Solution

Key Concept: $P(X<n)=\frac{n-1}{n}$, $P(X=n)=\frac{1}{n}$. This is geometric with $p=\frac{n-1}{n}$. Mean $=\frac{1}{p}=\frac{n}{n-1}$.

$n=10$.

Correct Answer: 10