Answer by Juliet for Understanding "randomness"

It might help to think of this in more discrete numbers. Consider want to generate random numbers between 1 and 36, so you decide the easiest way is throwing two fair, 6-sided dice. You get this:

     1    2    3    4    5    6  -----------------------------1|   1    2    3    4    5    62|   2    4    6    8   10   123|   3    6    9   12   15   184|   4    8   12   16   20   24   5|   5   10   15   20   25   306|   6   12   18   24   30   36

So we have 36 numbers, but not all of them are fairly represented, and some don't occur at all. Numbers near the center diagonal (bottom-left corner to top-right corner) will occur with the highest frequency.

The same principles which describe the unfair distribution between dice apply equally to floating point numbers between 0.0 and 1.0.