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| Math Central | Quandaries & Queries |
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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.
| 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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