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

(In reply to re: Thoughts by friedlinguini)

Assuming that Charadenine means 1) "the first digit of the page number, and 2) the probability that the first digit is any one of the given five (as opposed to separately calculating for each digit), here is how I would begin:

If all digits had the same probability, then the chances of one of the five given digits being the one is 5/10 = ½. But we ignore leading zeroes, and so the chances are actually increased to 5/9.

However, the nine digits are only evenly probable if the number of pages is [(10 ^ n) - 1]for some non-negative integer n. Otherwise the numbers between the highest page number and the next higher power of ten (minus one) do not contribute their first digits to the "pool"

(I'm not altogether certain what my next step should be, but if I decide on one I'll be back to continue posting.

Posted by TomM on 2002-07-03 12:56:52