For a randomly chosen real number x on the interval (0,10) find the exact probability of each:
(1) That x and 2x have the same first digit
(2) That x and x2 have the same first digit
(3) That x2 and 2x have the same first digit.
(4) That x, x2 and 2x all have the same first digit.
First digit refers to the first non-zero digit of the number written in decimal form.
(In reply to re: answers
"Since there are indeed an infinite number of points, the probability of an end point being chosen, even in the closed interval case, is zero."
You mean negligible, and may as well be zero.
I see that my initial observation was incorrect in that I incorrectly included/excluded those matches that began with zero and not a 'first non-zero' atch. My recalculation for (1) matched precisely with yours. My estimates for (2), (3) and (4) are at a difference, but probably due to errors in my calculations for the 'first non-zero' matches.
Posted by Dej Mar
on 2011-03-30 13:10:44