A wide variety of data sets such as tax returns, population sizes, and power consumption tend to comply with what is known as Benford’s law, which establishes a frequency distribution for the leading digits of data. For example, for the first leading digit, the law states the distribution should be

a) According to Benford’s law, are all numbers from 1 to 9 equally likely to occur as first digits?
b) What is the probability that the leading first digit of a randomly chosen number is a 1 or a 2 according to Benford’s law?

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1 First digit Probability 0.30 2 0.18 3 0.12 4 0.10 5 0.08 6 7 0.07 0.06 8 0.05 9 0.04