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 x^{2} have the same first digit
(3) That x^{2} and 2^{x} have the same first digit.
(4) That x, x^{2} and 2^{x} all have the same first digit.
First digit refers to the first nonzero 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 20110330 04:17:59 