Question

An urn contains n balls numbered 1 to n. If m balls are randomly withdrawn sequentially with replacement find P(X=k), k=1,2...m where m is the maximum of the m chosen numbers.

Answer 1

<img src="/cgi-bin/mimetex.cgi?P%28X=k,%20k=1,%20...,m%29%20=%20%5Cfrac%7B1%7D%7Bn%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7Bn%7D%20%5Ctimes%20...%20%5Ctimes%20%5Cfrac%7B1%7D%7Bn%7D%20=%20%5Cleft%20%28%5Cfrac%7B1%7D%7Bn%7D%20%5Cright%20%29%5Em" title="P(X=k, k=1, ...,m) = \frac{1}{n} \times \frac{1}{n} \times ... \times \frac{1}{n} = \left (\frac{1}{n} \right )^m">