If two dice are rolled, what is the probability the sum of the numbers is 4 or 5?
* i actually thought the two dice are the same and there is no difference between (1,4) (4,1). Then my answer was 4/36=1/9
But the answer is 7/36, apparently it considered the (1,4) (4,1) (2,3) (3,2) etc. Why should we think of the dice as different?
You have to consider those possibilities separately because, while there are two ways to get a 3 and a 1 to get a sum of 4, there’s only one way to get two 2s.
I think it’s easiest to understand this after seeing all the 36 possible rolls laid out:
Count all the 4s and 5s—there are 7 of them. If you ever get a dice probability question on the SAT (which you probably won’t), just take 20 seconds to draw that chart out, then count the cells you care about.