If two fair dice are​ rolled, what is the probability that the total showing is either even or less than ​four?

Question

If two fair dice are​ rolled, what is the probability that the total showing is either even or less than four?

Answer 1

I'm assuming the 'total' means that you're adding the two numbers you get from the two dice.

Size of the sample space: 6 x 6 = 36.

# cases, your total is even: this means either "both dices were even" or "both dices were odd". There are 9 cases where both dices roll even numbers, and additional 9 cases where both dices roll odd numbers, so there are total 18 cases here.

# cases, your total is less than 4: Well that's (1, 1), (1, 2), and (2, 1). Because we already counted (1, 1) when we were counting for the cases where your total is even, we are only counting 2 additional cases.

Probability of interest = (18 + 2) / 36 = 20/36 = 5/9