An ordinary (fair) die is a cube with the numbers
1
through
6
on the sides (represented by painted spots). imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. this sum is recorded as the outcome of a single trial of a random experiment.
compute the probability of each of the following events:
event
a
: the sum is greater than
9
.
event
b
: the sum is an odd number.
write your answers as exact fractions.

A die is a six-face solid and that rolling it twice will give us a sample space of 36 (calculated by multiplying 6 to itself). 

(1) The outcomes that the sum of the two numbers will be greater than 9 are listed below:
                         5 and 5, 5 and 6, 6 and 5, and 6 and 6
There are four and the probability is equal to 4/36 or 1/9.

(2) The outcomes that the sum is an odd number is listed below:
          1 and 2, 1 and 4, 1 and 6, 2 and 1, 2 and 3, 2 and 5, 3 and 2, 3 and 4, 3 and 6, 4 and 1, 4 and 3, 4 and 6, 5 and 2, 5 and 4, 5 and 6, 6 and 1, 6 and 3, 6 and 5
There are 18. Thus, the probability is 18/36 or 1/2.