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Bascule's Book (Posted on 2002-07-03) Difficulty: 5 of 5
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

See The Solution Submitted by Cheradenine    
Rating: 2.7500 (8 votes)

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re: Starting digit | Comment 35 of 40 |
(In reply to Starting digit by Warren Yamaguchi)

The logarithmic law of first digits is known as Benford's Law, and applies to various statistics, including measurements of natural phenomena. If book lengths were truly infinite in possibilities, then this law would apply, and the answer would be log(6) in base 10, which is 0.77815125... which truncates to the value you gave. Although books usually range from 120 to 1000 pages, we really don't have a good distribution function for them, and in its absence the best we have to go on is indeed Benford's Law.
  Posted by Charlie on 2003-02-03 09:26:06

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