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Probability (sample space)

  1. Sep 21, 2006 #1
    The question asks:

    Suppose that we randomly place 8 playing spieces on an 8 x 8 checkerboard.
    What is the probability that each row of the checkerboard will have only one piece?

    I've been trying forever to get this question going. My problem is that I cannot figure out the magnitude of the sample space. Can somebody please help me out with this?

    I tried to find the sample space for a 2x2 and 3x3 board.

    For a 2x2 board i got |S| = 6
    For a 3x3 board i got |S| = 24
    For a 4x4 board...it got really messy...

    Can somebody give me a boost please!? :uhh:
     
  2. jcsd
  3. Sep 21, 2006 #2
    well if theres 8x8 then the sample space is 8^2
     
  4. Sep 21, 2006 #3
    unless i did it wrong, for a 2x2 board 2^2 = 4 and not 6
    and for a 3x3 board, 3^2 = 9 and not 24
     
  5. Sep 21, 2006 #4
    well if you think about it...

    1 x x x
    2 x x x
    3 x x x
    1 2 3
     
  6. Sep 21, 2006 #5
    This is how i interpret it:

    . . .
    x x x
    x x x

    x x x
    . . .
    x x x

    x x x
    x x x
    . . .

    . x x
    x . .
    x x x

    . x x
    x x x
    x . .

    x . .
    . x x
    x x x

    x x x
    . x x
    . . x

    etc. etc..

    Which is more than 3^2 = 9

    What do you say?
     
  7. Sep 21, 2006 #6
    i say im not sure :P the sample space is still just the arena of outcomes, but your listing all the different outcomes from one sample space. its like the dice example, you have a 6x6 sample space but you can choose any number of combinations, but the sample space is still 6x6
     
  8. Sep 22, 2006 #7
    So can somebody please confirm what the sample space is?
     
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