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

Home > Probability
Evaluate probability (Posted on 2018-06-11) Difficulty: 3 of 5
If a and b are positive integers, find the probability that (a^2+b^2)/11 is a positive integer.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
analytical solution Comment 1 of 1
looking at x^2 mod 11 the possible remainders are

{0,1,3,4,5,9}


So we need two of these to add to a multiple of 11, since 9+9=18 is the largest sum the only possible multiples are 0 and 11.


The only way to get 0 is with 0+0 and there is no pair of values that add to 11.


Thus the only possible way for a^2+b^2 to be divisible by 11 is if both a and b are also divisible by 11.  Since each of these have a 1/11 chance of being divisible by 11 then the total probability is (1/11)^2 or 1/121

  Posted by Daniel on 2018-06-11 07:52:34
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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