The sample space of rolling two dice has 36 possible outcomes. Remember that the "sample space" is a set which contains all possible outcomes.
(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)
(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)
(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)
(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)
(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)
(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)
The probability of rolling a 2 is 1/36.
The probability of rolling a 3 is 2/36.
The probability of rolling a 4 is 3/36.
The probability of rolling a 5 is 4/36.
The probability of rolling a 6 is 5/36.
The probability of rolling a 7 is 6/36.
The probability of rolling an 8 is 5/36.
The probability of rolling a 9 is 4/36.
The probability of rolling a 10 is 3/36.
The probability of rolling an 11 is 2/36.
The probability of rolling a 12 is 1/36.
Event A: The sum is greater than 5.
Probability of rolling a number bigger than 5 is the sum of the probabilities of rolling a 6, 7, 8, 9, 10, 11, and 12.
5/36 + 6/36 + 5/36 + 4/36 + 3/36 + 2/36 + 1/36 = 26/36 which reduces to 13/18
Event B: The sum is an odd
The probability that the sum is odd is 50%.
Sum = 3, 5, 7, 9, 11
P(B) = 18/36 = 50%