# Probability of a given number of a set of random numbers

## Homework Statement

Each week you receive a random number {1,...,n}. You may receive the same number more than once. Each number has 1/n probability of being sent to you. What is the expected amount of time until you receive the number 6?

## Homework Equations

I'm not sure what to use here.

## The Attempt at a Solution

The probability of receiving any number for the first time at the kth week should be $$(1-1/n)^{k-1}/n$$.