(essay question 7 points)
suppose you roll a six-sided die two times hoping to get two numbers whose sum is even. what is the sample space? how many favorable outcomes are there?

Well I don't know.
Let's think about it:

-- There are 6 possibilities for each role.
    So 36 possibilities for 2 rolls.
    Doesn't take us anywhere.

New direction:
-- If the first roll is odd, then you need another odd on the second one.
-- If the first roll is even, then you need another even on the second one.
This may be the key, right here !

-- The die has 3 odds and 3 evens.

-- Probability of an odd followed by another odd = (1/2) x (1/2) = 1/4
-- Probability of an even followed by another even = (1/2) x (1/2) = 1/4

I'm sure this is it.  I'm a little shaky on how to combine those 2 probs.

Ah hah ! 
Try this:

Probability of either 1 sequence or the other one is (1/4) + (1/4) = 1/2 .

That means ... Regardless of what the first roll is, the probability of
the second roll matching it in oddness or evenness is 1/2 .

So the probability of 2 rolls that sum to an even number is 1/2 = 50% .

Is this reasonable, or sleazy ?

Patrick earns the most money per hour