1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Chance of 2 overlapping matrices

  1. Apr 9, 2008 #1
    [SOLVED] chance of 2 overlapping matrices

    I have a simple problem, but I'm not sure if my answer is correct :P.
    I have a matrix, like this:

    0 0 0 0 1
    0 1 0 0 0
    0 0 0 0 0
    0 0 0 1 0
    0 0 0 0 0

    i.e. an axb matrix, with c 'ones'. If I now take another matrix, with the same size, what's the probability that d 'ones' are on the same spot?
    I thought like this:
    the chance that 1 'one' is on the same spot is 1/(ab)
    the chance that the 2nd 'one' is on the same spot is 1/(ab-1), etc.
    the order is not important, so if the 2nd matrix also has c ones, we add a factor of c!

    So the chance that a 2nd matrix has d 'ones' (d<c) on the same spot as the first matrix is
    [tex]\frac{c!}{d!(c-d)!}\prod_{i=0}^{c-1}\frac{1}{ab-i}[/tex]

    But i'm not feeling completely comfortable with this. Say matrix 1 has 4 ones. Matrix 2 may have 6 ones, but a maximum of 4 on the same place. (in reality, approximately 99% of the matrix are zeros). Is this still a correct way then?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted