### Instruction: Two standard 6-sided dice are tossed. What is the probability that the sum of the numbers shown on the dice is a prime number? Express your answer as a common fraction.### Response: I know that the possible sums of two dice range from 2 to 12, and there are 36 equally likely outcomes.
I can list the prime sums: 2, 3, 5, 7, and 11.
I can also count how many ways to get each prime sum.
For 2, there is only one way: 1 and 1.
For 3, there are two ways: 1 and 2, or 2 and 1.
For 5, there are four ways: 1 and 4, 4 and 1, 2 and 3, or 3 and 2.
For 7, there are six ways: 1 and 6, 6 and 1, 2 and 5, 5 and 2, 3 and 4, or 4 and 3.
For 11, there are two ways: 5 and 6, or 6 and 5.
So the total number of ways to get a prime sum is 1 + 2 + 4 + 6 + 2 = 15.
Therefore, the probability of getting a prime sum is 15/36, which can be simplified to 5/12.