Example 4.13

EXAMPLE 4.13 First digits That Are Equally Likely

You might think that first digits in business records are distributed “at random” among the digits 1 to 9. The nine possible outcomes would then be equally likely. The sample space for a single digit is

Because the total probability must be 1, the probability of each of the nine outcomes must be 1/9. That is, the assignment of probabilities to outcomes is

First digit	1	2	3	4	5	6	7	8	9
Probability	1/9	1/9	1/9	1/9	1/9	1/9	1/9	1/9	1/9

187

The probability of the event that a randomly chosen first digit is 3 or less is

Compare this with the Benford's law probability in Example 4.11 (page 185). A crook who fakes data by using “random” digits will end up with too few first digits that are 3 or less.