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Probability Puzzle

  1. Sep 9, 2010 #1
    On average, how many times do you need to roll six dice together to see all six different numbers turn up within a single such group roll?
     
  2. jcsd
  3. Sep 9, 2010 #2

    CompuChip

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    64.8 times?
     
  4. Sep 13, 2010 #3
    I agree, except for the .8 :)
     
  5. Sep 13, 2010 #4

    Jonathan Scott

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    I agreed with 64.8, for the following reasons:

    There are 6! ways of throwing all six values and 66 possible results, so the probability in each throw is 6!/66 = (1*2*3*4*5*6)/(6*6*6*6*6*6) = (4*5)/(6*6*6*6) = 5/(3*3*6*6) = 5/324.

    The average interval between such throws (or, as in this case, before the first such throw) is therefore the reciprocal of this, 324/5 = 64.8, as usual for a Poisson distribution.
     
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