Level: Intermediate, Version: FM 12 or later

Benford’s Law

A common exercise in freshman courses on statistics and probability is to divide the students into two groups, let’s call them A and B.

8-11-2013 9-39-15 PMEach student in group A is instructed to flip a coin 100 times and record the resulting sequence of heads and tails. Each student in group B is instructed to merely pretend to have done so, and write down the fictional sequence. The sequences are submitted anonymously to the professor, but invariably the professor correctly determines which group they belong to.

Take a look at the example at right. If you were the professor would you assume it comes from group A or from group B? Would it strike you as suspicious that the first six tosses alternate between T and H with perfect regularity, or that starting with toss 12, there are five H’s in a row?

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