Bascule is reading a book. What is the probability that the first digit of the page he is on is 1, 2, 3, 4 or 5?

a) obtain an expression
b) approximate a numerical value

Let N be the number of pages in the book. Let p be the probability that the first non-zero digit of the page number is in the set {1,2,3,4,5}.

if 1 <= n <= 5, p = 1
if 6 <= n <= 9, p = 5 / n
if 10 <= n <= 59, p = (n - 4) / n
if 60 <= n <= 99, p = 55 / n
if 100 <= n <= 599, p = (n - 44) / n
if 600 <= n <= 999, p = 555 / n
if 1000 <= n <= 9999, p = (n - 444) / n
and so forth.

If you want a single answer, you need to know something about the distribution of page count in the books that Bascule reads.

Posted by Jim Lyon on 2002-07-03 13:03:25