Here is a simple problem in probability.

(1) Pick a number *k* between 1 and 9. Assume all digits are equally likely.

(2) Pick a number *m* in the range from 1 to *k*.

**What is the probability distribution for the number m?**

A graph of the probability distribution is shown in the figure here.

Can you derive a formula for this probability distribution?

Can you generalise it to the range from 1 to 10^n?

Can you relate this problem to Benford’s Law [described here]?

Solution, and more on Benford’s Law, next week.