! We want to extimate what fraction of items in a 
  certain population are Red.
How big a sample size do we need as a function of:
   M = population size,
   F = actual, but unknown to us, fraction of the population that is Red,
   N = our sample size,
   R = resulting number (a random variable) of items in our sample that are Red,
   P = R/N = our estimate of the fraction items that are Red in the population,
   T = Target standard deviation for P that we specify.
Then, based on the Hypergeometric distribution:
  Var( R) = N*F*M*(M-F*M)*(M-N)/(M*M*(M-1))
                   = N*F*(1-F)*(M-N)/(M-1)
  Var(P) =  Var( R)/( N*N) = F*(1-F)*(M-N)/(N*(M-1))
If we want our estimator to have some specified target standard deviation T or less,
( implies variance of T*T) this means we want to solve:
  T*T = F*(1-F)*(M-N)/(N*(M-1)), or if we multiply through by N:
  N*T*T= F*(1-F)*(M-N)/(M-1), or
  N*(T*T + F*(1-F)/(M-1)) = F*(1-F)*M/(M-1), or
  N  = (F*(1-F)*M/(M-1))/ (T*T + F*(1-F)/(M-1)),
As M goes to infinity, notice that 
   N approaches (from below): (F*(1-F))/(T*T);

! Keywords: Chart, ChartPCurve, Graph, Hypergeometric distribution, Sampling;

!Let's do some plotting.
! Compute the required sample size, given M, F, and T;
     N = (F*(1-F)*M/(M-1))/(T*T + F*(1-F)/(M-1));
   F = 0.5;  ! F = 0.5 is the obvious/worst case Null/strawman hypothesis;
   T = 0.05;
   ATOTE = (F*(1-F))/(T*T) ;
   MUL = 500;  ! Upper limit on N for plotting purposes;
 ! Generate a chart;
        @CHARTPCURVE( 'How Big a Sample Do We Need for T = ' +@FORMAT(t,"4.2f")+'  F = '+@FORMAT(F,"4.2f")+
            ' (Asymptote= '+ @FORMAT( ATOTE,"5.0f")+')',
            'Population Size','Sample Size',
            SAMPSIZE, M, 2, MUL, 'SampSize vs PopSize', N);