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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

    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
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