The first step is to create the write out the probability space. For each possible product, list the values on each die that will give that product. Each such outcome has a probability of 1/36 and so you can calculate the probability of each of the numbers on the card as follows:
1: (1,1) prob = 1/36
2: (1, 2), (2, 1) prob = 2/36
3: (1, 3), (3, 1) prob = 2/36
4: (1, 4), (2, 2), (4, 1) prob = 3/36
5: (1, 5), (5, 1) prob = 2/36
6: (1, 6), (2, 3), (3, 2), (6, 1) prob = 4/36
8: (2, 4), (4, 2) prob = 2/36
9: (3, 3) prob = 1/36
10: (2, 5), (5, 2) prob = 2/36
12: (2, 6), (3, 4), (4, 3), (6, 2) prob = 4/36
15: (3, 5), (5, 3) prob = 2/36
16: (4, 4) prob = 1/36
18: (3, 6), (6, 3) prob = 2/36
20: (4, 5), (5, 4) prob = 2/36
24: (4, 6), (6, 4) prob = 2/36
25: (5, 5) prob = 1/36
30: (5, 6), (6, 5) prob = 2/36
36: (6, 6) prob = 1/36
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