title: Probability of selecting an element from a set
body: <p>The expected probability of randomly selecting an element from a set of n elements is P=1.0/n .
  Suppose I check P using an unbiased method sufficiently many times. What is the distribution type of P? It is clear that P is not normally distributed, since cannot be negative. Thus, may I correctly assume that P is <a href="http://en.wikipedia.org/wiki/Gamma_distribution" rel="nofollow noreferrer">gamma distributed</a>? And if yes, what are the parameters of this distribution? 
  Histogram of probabilities of selecting an element from 100-element set for 1000 times is shown <a href="http://img267.imageshack.us/my.php?image=imageqa2.png" rel="nofollow noreferrer">here</a>.</p>
  
  <p>Is there any way to convert this to a standard distribution</p>
  
  <p>Now supposed that the observed probability of selecting the given element was P* (P* != P). How can I estimate whether the bias is statistically significant?</p>
  
  <p>EDIT: This is not a homework. I'm doing a hobby project and I need this piece of statistics for it. I've done my last homework ~10 years ago:-) </p>