The easiest way to work out probablilities with 2 dice is to draw up a 6 by 6 grid.
Die 2 is down the side
Die 1 is acros the top and
1 | 2 | 3 | 4 | 5 | 6 | |
1 | 1,1 | 2,1 | 3,1 | 4,1 | 5,1 | 6,1 |
2 | 1,2 | 6,2 | ||||
3 | 1,3 | 6,3 | ||||
4 | 1,4 | 6,4 | ||||
5 | 1,5 | 6,5 | ||||
6 | 1,6 | 2,6 | 3,6 | 4,6 | 5,5 | 6,6 |
The red ones are the combinations that work. There are 20 of them
So
P(of a 6 OR a 1) = 20/36 = 5/9