Question

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

Answer 1

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.