### Instruction: Two fair, six-sided dice are rolled.  What is the probability that the sum of the two numbers showing is less than 11?### Response: To find the probability of an event, I need to divide the number of favorable outcomes by the total number of possible outcomes.
In this case, the total number of possible outcomes is 36, since there are 6 ways to roll each die and the outcomes are independent.
To count the favorable outcomes, I can think of the different sums that are less than 11 and how many ways to get them.
For example, the sum can be 2, 3, 4, 5, 6, 7, 8, 9, or 10.
The sum of 2 can only happen if both dice show 1, so there is 1 way to get that.
The sum of 3 can happen if one die shows 1 and the other shows 2, or vice versa, so there are 2 ways to get that.
The sum of 4 can happen if one die shows 1 and the other shows 3, or vice versa, or if both dice show 2, so there are 3 ways to get that.
Similarly, the sum of 5 can happen in 4 ways, the sum of 6 can happen in 5 ways, the sum of 7 can happen in 6 ways, the sum of 8 can happen in 5 ways, the sum of 9 can happen in 4 ways, and the sum of 10 can happen in 3 ways.
Adding up these numbers, I get 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 = 33.