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 First Steps? by TomM)

In most problems of this kind, if you assume an even distribution over the range, you can use the probability associated with the average value to approximate that associated with the total. In this case, that would mean that we would assmue the average book with between (10^n) and [(10^[n+1])-1] pages has [5(10^n)]pages and work with the probabilities that presents.

The problem is that it won't work in this case, because the numbers added to/removed from the pool as we move from the average to the extremes do not affect the chances in the same way. As you move closer to (10^n), you remove "good" numbers from the pool. As you move closer to [(10^[n+1])-1], you add "bad" numbers. In both cases, you wind up with a pool with a lower probability of success than the average number of pages gives, so the average is not a good approximation of the total. If the looked-for digits were 1, 2, 8, and 9 it would work, but not with 1, 2, 3, 4, and 5.

Posted by TomM on 2002-07-03 14:09:55