The number of possible outcomes of throwing 2 dice together is 36, but only 2 of these outcomes add up to 3: 1+2 or 2+1. So the probability is 2/36=1/18.
A probability distribution of all possibilities is given through the table below:
| 1+1=2 |
1+2=3 |
1+3=4 |
1+4=5 |
1+5=6 |
1+6=7 |
| 2+1=3 |
2+2=4 |
2+3=5 |
2+4=6 |
2+5=7 |
2+6=8 |
| 3+1=4 |
3+2=5 |
3+3=6 |
3+4=7 |
3+5=8 |
3+6=9 |
| 4+1=5 |
4+2=6 |
4+3=7 |
4+4=8 |
4+5=9 |
4+6=10 |
| 5+1=6 |
5+2=7 |
5+3=8 |
5+4=9 |
5+5=10 |
5+6=11 |
| 6+1=7 |
6+2=8 |
6+3=9 |
6+4=10 |
6+5=11 |
6+6=12 |
FREQUENCY DISTRIBUTION (OCCURRENCES):
| 2 |
1 |
| 3 |
2 |
| 4 |
3 |
| 5 |
4 |
| 6 |
5 |
| 7 |
6 |
| 8 |
5 |
| 9 |
4 |
| 10 |
3 |
| 11 |
2 |
| 12 |
1 |
The first column is the sum of the dice and the second is the number of ways that sum can be made.
From the frequency distribution we get the triangular probability distribution:
The dotted line just shows the general triangular shape of the distribution. The horizontal markings are the dice sums and the vertical markings are the number of occurrences. The fractions show the probabilities, which sum to 1 (100%) so the area of the triangle is 1 when measured in terms of the probabilities (NOT by counting squares!).
From the table we can see that the probability of either die being 3 is as follows (probabilities in brackets: 1/6 = chance of a 3, 5/6 = chance of some other number):
No 3's: 25 (25/36=5/6*5/6)
One 3: 10 (10/36=5/18=5/6*1/6+1/6*5/6)
Two 3s: 1 (1/36=1/6*1/6)
TOTAL 36 (1)