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Counting for probability

  1. Aug 27, 2011 #1
    1. The problem statement, all variables and given/known data

    "Find the probability of the sum of three rolled die being less than or equal to 9."

    Given problems like this, my question is: is there some way to find the answer besides writing out all 216 combinations and then counting the ones that equal 9? I feel like there is, but I'm just being blind.
  2. jcsd
  3. Aug 27, 2011 #2


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    You could consider the total as being the sum of two dice and the third. Presumably, you know the probabilities involved with rolling two dice.

    For example, the probability of rolling a 3 would be P(first two=2)xP(last die=1) = (1/36)(1/6) = 1/216.
  4. Aug 27, 2011 #3
    Ah, that looks good. Thanks!
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