If you roll two regular dice, what is the probability that at least one of the numbers is more than three?
Solution:
There are six possible outcomes for rolling a dice. If we are rolling two dice then we can make a grid showing all the possible outcomes. There are 36 in total. In the table below you can clearly see that, of the 36 possible outcomes, there are nine for which neither number is over three, and 27, for which at least one is.
| 1 | 2 | 3 | 4 | 5 | 6 | |
| 1 | no | no | no | yes | yes | yes |
| 2 | no | no | no | yes | yes | yes |
| 3 | no | no | no | yes | yes | yes |
| 4 | yes | yes | yes | yes | yes | yes |
| 5 | yes | yes | yes | yes | yes | yes |
| 6 | yes | yes | yes | yes | yes | yes |
If you roll two regular dice, the probability that at least one of the numbers is more than three is 27/36, or 3/4.