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Puzzle: probability of matching dice

March 26, 2007 am31 7:20 am

I threw three identical dice on the table and looked at the outcome. If I throw them again, what is the probability I get the same outcome?

Note: the language is intentionally ambiguous. What are the two possible interpretations? Make certain you know which interpretation of the problem you are solving before you solve. Use the comments, section, below, to talk about the problem without solving it. Use this solutions page to provide solutions.

(There is a hint below the fold —>)

Getting the same exact dice and getting the same sum are different problems. For example, if the roll was 2/2/2 the probability of getting the same 3 dice is 1/216, but the probability of getting a 6 is 10/216.

To get a feel for this problem, it might help to solve the 2 dice version.

One Comment leave one →
  1. March 27, 2007 pm31 11:27 pm 11:27 pm

    one possibility… each of the dice comes up with it’s exact same number again… so you would calculate the probabilty separately for each die, then multiply them… other possibility, you get the same three numbers, but not necessarily on the same dice… so you calculate the total number of possible three-digit combinations, then figure out how likely any specific one of them is… I think.

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