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

1. Feb 25, 2007

### Dragonfall

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
I'm not sure what to use here.

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

2. Feb 26, 2007

### bigplanet401

Try computing the expectation value of k.

3. Feb 26, 2007

### Dragonfall

I did, I get n, where everyone else seems to get n-1.