Answer :
EVENT A.
We have to count in how many possible ways does the sum of the two rolls of the die add up to more than 7. The possibilities are:
6+2
6+3
6+4
6+5
6+6
5+3
5+4
5+5
5+6
4+4
4+5
4+6
3+5
3+6
2+6
Then, there is 15 ways that the sum os greater than 7. Now we have to calculate how many combinations there is in total, which is 6 possible outcomes for the first roll and other 6 for the second roll, then there is 6x6=36 possible outcomes.
The probability for event A is then 15/36 or 5/12
EVENT B:
In a similar way, we have to count how many ways there is such that the sum is even:
1+1
1+3
1+5
2+2
2+4
2+6
3+1
3+3
3+5
....
We notice that there is 3 ways for each number from the first roll. Then the total is 6*3=18 ways such that the sum is even. The total possible outomes is 6x6=36.
Hence the probability for Evenet B is 18/36 or 1/2
