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    Question Probability




    You have been put in charge of developing a new game of chance. In this game a person will roll two cubes each having the numbers 1 to 6 on their faces. After rolling the cubes the smaller number is subtracted from the larger. (This keeps us from getting negative number answers.) As a first step in developing the game, what are the possible outcomes and their probabilities?

    Thanks so much!

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    Since we are subtracting the smaller from the larger number, the possible outcomes are 0,1,2,3,4,5.

    We have 0 if the cubes are (1,1), (2,2), (3,3)...(6,6)
    We have 1 if the cubes are (1,2), (2,1), (2,3), (3,2)...(5,6), (6,5)
    We have 2 if the cubes are (1,3), (3,1), (2,4), (4,2)...(4,6), (6,4)
    ...

    Each pair have probability of (1/6)(1/6)=1/36. You can count the number of pairs for each outcome, multiply by 1/36, and get the probability of outcomes.

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