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: part (1) not so hard after all (spoiler)
Thanks for the correction. I've amended the original comment with the correction and appropriate attribution to your finding it.
I'm still at a loss for the discrepancy between the analytic and simulation solutions for part 3.
Posted by Charlie
on 2011-03-30 10:57:13