Paradoxes of Probability

The concept of throwing balls at bins to test randomness can be discussed. This is covered in my paper How Computers Generate Random Numbers
  1. If all the balls fall into one bin, according to Probability Theory it's just as likely as any other outcome, but it doesn't make us feel good that our assumption that each bin was equally likely was correct.
  2. Likewise, if each bin ends up with exactly the same number of balls it should also make us feel bad. In this case each throw is probably not independent of all previous throws.
Interesting Paradoxes of Probability are covered at These paradoxes can be covered at a conceptual level without doing any of the math.

This would also be a good time to recommend the classic book
cover How to Lie With Statistics by Darrell Huff, Irving Geis (Illustrator)

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