Stats
posted by MT .
I roll a pair of fair dice and compute the number of spots on the two sides facing up. Denote this total by X. The probability distribution of X is
X Prob
2 1/36
3 2/36
4 3/36
5 4/36
6 5/36
7 6/36
8 5/36
9 4/36
10 3/36
11 2/36
12 1/36
The probability that X is an even number is

An even number is any of 2,4,6,8,10,and 12 (within the sample space above).
So the probability of throwing a sum equal to an even number is the sum of the corresponding probabilities, namely:
1/36+3/36+5/36+...1/36.