Brian plays a game in which two fair, six-sided dice are rolled simultaneously. For each die, an even number means that he wins that amount of money and an odd number means that he loses that amount of money. What is the probability that Brian makes money on his first roll?
11/12
7/12
1/2
5/12
1/3
Please simplify your explanation
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Here are the combinations of winners so you can see (there are 36 total possible outcomes 6 x 6):
2, 2
2, 4
2, 6
4, 2
4, 4
4, 6
6, 2
6, 4
6, 6
2, 1
4, 1
4, 3
6, 1
6, 3
6, 5
1, 2
1, 4
3, 4
1, 6
3, 6
5, 6
21/36 = 7/12
There are other ways to do this, of course, but sometimes brute force can take only 30-45 seconds and is worth doing...
2, 2
2, 4
2, 6
4, 2
4, 4
4, 6
6, 2
6, 4
6, 6
2, 1
4, 1
4, 3
6, 1
6, 3
6, 5
1, 2
1, 4
3, 4
1, 6
3, 6
5, 6
21/36 = 7/12
There are other ways to do this, of course, but sometimes brute force can take only 30-45 seconds and is worth doing...
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