### Instruction: Two dice are tossed. What is the probability that the sum is greater than three?### Response: I need to find the number of ways to get a sum greater than three, and divide it by the total number of possible outcomes.
The total number of possible outcomes is 6 times 6, since each die can show any of the six numbers independently.
So the denominator of the probability is 36.
To get a sum greater than three, I need to avoid the cases where the sum is two or three.
The only way to get a sum of two is to roll two ones, which has a probability of 1/36.
The only ways to get a sum of three are to roll a one and a two, or a two and a one, which have a combined probability of 2/36.
So the probability of getting a sum of two or three is 1/36 + 2/36 = 3/36.
Therefore, the probability of getting a sum greater than three is the complement of that, which is 1 - 3/36 = 33/36.