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problem with RandomInteger

Hello Mathgroup,

  I have recently encountered a strange behavior of RandomInteger
function when used inside Module construct. Here is an example:

str1[] := Module[{l, i, j},
  l = {0, 0, 0};
  i = RandomInteger[{1, 3}];
  l[[i]] = 1;
  j = RandomInteger[{1, 3}];
In[3]:= N[Total[Table[str1[],{200}]]]/200
Out[3]= 0.345

which is reasonably close to 1/3, but

In[5]:= N[Total[Table[str1[],{1000}]]]/1000
Out[5]= 0.997

looks very strange. What's happening here?

TIA, Yuri.

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