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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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Starting digit | Comment 34 of 41 |
Since the size of the book can be any random number it's obvious that more pages will start with the digit one as any higher number. Similar for the digit 2 and all higher numbers. No pages can start with zero. So there's only 9 possible starting digits with the p(1) > p(2) > p(3) > p(4) > p(5) > p(6) > p(7) > p(8) > p(9). We also know the sum of the p(1-9) = 100%.

I hypothesize that the probability of pages starting with one is the log of 2 (in base 10) and the probability of starting with one or two is the log of 3 (in base 10). Up to starting with 1-9 is the log of 10 (base 10) which is 1.00.

At least the endpoints seem to work. Under these conditions, the probability of a page starting with the digits 1-5 is log of 6 (base 10). Without knowing what that is I approximate the answer to be the sum of log 2 and log 3 (since 2x3=6) or if I remember correctly I think it's .3010 + .4771 = .7781.
  Posted by Warren Yamaguchi on 2003-01-25 22:47:56
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