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Equally Likely Outcomes Distribution

Let there be a set $S$ with $N$ elements, each of them having the same probability. Then

$\displaystyle P(S)$ $\textstyle =$ $\displaystyle P\left({\,\bigcup_{i=1}^N E_i}\right)= \sum_{i=1}^N P(E_i)$  
  $\textstyle =$ $\displaystyle P(E_i) \sum_{i=1}^N 1 = NP(E_i).$  

Using $P(S) \equiv 1$ gives

\begin{displaymath}
P(E_i) = {1\over N}.
\end{displaymath}

See also Uniform Distribution




© 1996-9 Eric W. Weisstein
1999-05-25