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- There are (6 x 6) = 36 possible results of rolling 2 dice.

- There are 27 outcomes where the product is an even number:

1 - 2, 1 - 4, 1 - 6

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

3 - 2, 3 - 4, 3 - 6

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

5 - 2, 5 - 4, 5 - 6

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

- The probability of success is 27/36 = 75%

- The odds are 3 to 1 in favor.

The nice thing about calculations with 2 dice, is it's fairly simple to tally up the results on a table (6 x 6 = 36 entries). But for more complex problems, a formula is much easier. Here's how to develop a formula for this problem:

If either one or both of the dies have an even number, the product will be even. It's easier to figure probability of not getting even, then subtract from 1. Both dies must have an odd number for this to occur. So P1odd = ½ and P2odd = ½. Since both event have to occur, we multiply them together: (½)(½) = ¼. So the chances of getting an odd product is ¼, or 25%. The chance of getting even is (1 - ¼), which is ¾, or 75%.

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Q: What are the odds of rolling 2 dice whose product is an even number?
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