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

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