You have two fair, six-sides dice. However, the dice have been modified so that instead or 1,2,3,4,5,6 the sides are numbered 1,2,2,2,3,4.

What is the probability the total of the two dice is an even number?

5/9.

Step-by-step explanation:

Prob (first dice = 2 and second = 2) = 1/2 * 1/2 = 1/4

Prob (first = 2, second = 4) = 1/2 * 1/6 = 1/12

Prob (first = 4 and second = 2) = 1/12.

Prob (first = 3 and second = 1) = 1/36

Prob (first = 1 and second = 3) = 1/36.

Prob (first = 3 and second = 3) = 1/6 * 1/6 = 1/36.

Prob (first = 1 and second = 1 = 1/36.

Prob (first = 4 and second = 4 = 1/36.

Required probability is the sum of these which is:

5/9.

I hope I've thought of all the possible outcomes.