For a randomly chosen real number x on the interval (0,10) find the exact probability of each:

(1) That x and 2^x have the same first digit

(2) That x and x² have the same first digit

(3) That x² and 2^x have the same first digit.

(4) That x, x² and 2^x all have the same first digit.

First digit refers to the first non-zero digit of the number written in decimal form.

As a real number line has an infinite number of points an exact probability can not be given for a randomly chosen real number but only an approximation. As we are given the notation for the interval as (0,10) and not [0,10], both endpoints, 0 and 10, are excluded.

An approximation for each is given:
(1) 0.05443...
(2) 0.19830...
(3) 0.28425...
(4) 0.0152...

Edited on March 30, 2011, 12:03 pm

Posted by Dej Mar on 2011-03-30 04:17:59