Binomial Probability Equation for first 28 patterns from Dr. Ivan Panin

PROVERBS 25:2 It is the glory of God to conceal a thing: but the honour of kings is to search out a matter.

probability website

(k) times occurring out of (n) opportunities with (p) possibilities

how many (k) do occur (n) can occur (p) reciprocal of should occur

      n!
------------ * ((1/p)^k)((1-(1/p))^(n-k))
k!(n-k)!

var show = "";
//__________________________________________________________________
function knp(k1,n,p)
{
   var sum = 0;
   for (var k = n; k >= k1; k--)
   {
      var a = factorial(n) / (factorial(k) * factorial(n-k));
      var b = Math.pow(1/p,k)
      var c = Math.pow(1 - (1/p),n-k);
      sum += a * b * c;
   }
   show += Math.floor(1/sum) + " * ";
   return(1/sum);
}//__________________________________________________________________
function total()
{
   show = "";
   var sum = 1.0;
   sum *= knp(1,1,7);
   sum *= knp(7,28,7);
   sum *= knp(1,1,2401);
   sum *= knp(1,1,16807);
   sum *= knp(1,1,343);
   sum *= knp(1,7,2401);
   alert(show + " = " + sum);
}
//__________________________________________________________________
function factorial(f)
{
   var out = 1;
   for (var i = 1; i <= f; i++)
   {
      out *= i;
   }
   return(out);
}
//__________________________________________________________________



k
n
p




Theoretical and emperical differ because of distribution anomalies.

Emperical data is from testing 27,288,799 psuedo sentences from http://www.textfiles.com/etext/FICTION/