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    A user wants to play a guessing game with 2 dices, they throw it, Here are all the different combinations of numbers they can get:

    1,1 2,1 3,1 4,1 5,1 6,1
    1,2 2,2 3,2 4,2 5,2 6,2
    1,3 2,3 3,3 4,3 5,3 6,3
    1,4 2,4 3,4 4,4 5,4 6,4
    1,5 2,5 3,5 4,5 5,5 6,5
    1,6 2,6 3,6 4,6 5,6 6,6

    There are 4 different possibilities of the user rolling 6 meaning a 4/36 = 1/9.

    The question I want to ask here is there any possible formula one can use to determine the number of possibilities as opposed to actually counting the possibilities.

    There are 2 formulas but I’m not sure which one is required:
    Classical formula is that of:
    P(A)= (Number of Ways A can occur)/(The Number of ways experiment can proceed)

    Frequency based is that of :
    P(A)=(Number of Times A occured)/(Number of ways experiment was run)

    I understand that the frequency based approach is more suited for research with a data sample but couldn’t it be applied here as we have a data sample, in other words the possibilities of rolls??

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Updated: January 14, 2010

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