EXAMPLE 4.15

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

S = {1, 2, 3, 4, 5, 6, 7, 8, 9}

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

The probability of the event B that a randomly chosen first digit is 7 or more is

Compare this with the Benford’s law probability in Example 4.13. A person who fakes data by using “random” digits will end up with too many first digits that are 7 or more.