1. ## 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!

2. 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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