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B Calculating Probabilities of a dice roll

  1. Mar 16, 2016 #1
    I'm trying to figure out how to correctly workout the probability of rolling 3 6's if I roll 4 dice at a time. If I roll 3 sixes in a row, I don't bother with the last roll
    The order in which I roll them doesn't matter
    So here are my potential combinations
    Combination 1 => x 6 6 6
    Combination 2 => 6 x 6 6
    Combination 3 => 6 6 x 6
    Combination 4 => 6 6 6

    Combination 1/2/3 are the same - I used 5/6 on the first roll because i'm assuming I didn't roll a six
    (5/6) (1/6) (1/6) (1/6) = (5/1296) = 0.0039
    Combination 4
    (1/6) (1/6) (1/6) = (1/216) = 0.0046

    I add up the different combinations of rolling the 6s
    3(0.0039) + 0.0046 = 0.0163
    My odds of rolling 3 sixes on 4 rolls is 0.0163

    Did I do this correctly?
     
  2. jcsd
  3. Mar 16, 2016 #2

    jbriggs444

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    Science Advisor

    Yes. That is one correct way to proceed. Arranging things so that x is always in the range 1-5 avoids the pitfall of double-counting certain cases. You have successfully accounted for the 4-sixes case as one of the underlying possibilities for case 4.
    Rounding in the calculation means that your last digit is incorrect, but it is only off by one.
     
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