First of all, note that there are 36 possible outcomes (all the numbers from 1 to 6 from the first die, combined with all the numbers from 1 to 6 from the second die).
a. Out of these 36 outcomes, the only ways to get 8 as sum are: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2). There are 5 favourable cases over 36 possible cases, so the probability is 5/36.
b. We want to get 8 as sum, and the first die must be a 2. Out of the five pairs we got before, only the first satisfies this request, so the probability is 1/36
c. Knowing that the first die was a 2, we have 6 possible outcomes:
The second die rolls a 1, for a total of 3.
The second die rolls a 2, for a total of 4.
The second die rolls a 3, for a total of 5.
The second die rolls a 4, for a total of 6.
The second die rolls a 5, for a total of 7.
The second die rolls a 6, for a total of 8.
So, there is 1 favourable outcome out of 6 possible outcomes, so the probability is 1/6
d. The die is fair, so every number occurs with probability 1/6.
