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Question from dave, a student:

I don't understand how to do this: Two fair dice are rolled. What is the probability that the difference of the squares of the numbers is divisible by three? the answer is 5/9

Dave,

I would just write them down and count. If you organize them in a table this is straightforward.

The top row is the first die and the left column is the second die. In the body of the table is the non-negative difference of squares. Complete the table and count how many are divisible by 3.

Difference of squares

  1 2 3 4 5 6
1 0 3 8 15 24 35
2 3 0 5 12 . .
3 8 . . . . .
4 . . . . . .
5 . . . . . .
6 . . . . . .

Harley

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