All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
Powerful Digit (Posted on 2011-03-29) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Jer    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3): answers Comment 12 of 12 |
(In reply to re(2): answers by Dej Mar)

"You mean negligible, and may as well be zero."

I mean: Integral{10 to 10} (any function) dx = 0, as the antiderivative at 10 is subtracted from itself, and even in a discontinuous function with no proper antiderivative, the width of the Riemann sum element has gone to the limiting case of 0.

Of course in limited precision simulations, there would be a finite chance of zero or 10 as only a finite number of decimal or binary places are randomized. But in theory the probability is indeed zero.

  Posted by Charlie on 2011-03-30 14:20:40
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information