Two dice are tossed. What is the probability that the sum of both dice is a prime number?

This is what I have so far
Presuming two fair, 6-sided dice, each numbered 1 through 6:

You can achieve one of the following results on any given roll: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. But there is only 1 way to get a 2, 2 ways to get a 3, 3 ways to get a 4, up to 6 ways to get a 7, then 5 ways to get 8, and so on. Total is 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 36 possible outcomes.

The prime numbers from 2 through 12 inclusive are: 2, 3, 5, 7, and 11. There is 1 way to get a 2, 2 ways for a 3, 4 ways for a 5, 6 ways for a 7 and 2 ways for 11. Total of 1 + 2 + 4 + 6 + 2 = 15 successful outcomes out of 36 possible outcomes.

Your reasoning and calculations are correct. So the probability of getting a prime number as the sum is 15/36.

You have correctly identified the total number of possible outcomes when two dice are tossed, which is 36 (since each die has 6 possible outcomes and there are two dice).

To determine the number of successful outcomes (i.e., when the sum of both dice is a prime number), you correctly identified that the prime numbers from 2 to 12 (inclusive) are 2, 3, 5, 7, and 11.

Now, let's calculate the number of ways to achieve each prime sum:

- To get a sum of 2, there is only one combination: (1, 1).
- To get a sum of 3, there are two combinations: (1, 2) and (2, 1).
- To get a sum of 5, there are four combinations: (1, 4), (2, 3), (3, 2), and (4, 1).
- To get a sum of 7, there are six combinations: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).
- To get a sum of 11, there are two combinations: (5, 6) and (6, 5).

Adding up the number of combinations for each prime sum, we get a total of 1 + 2 + 4 + 6 + 2 = 15 successful outcomes.

Therefore, the probability of getting a sum of both dice that is a prime number is 15/36, which can be simplified to 5/12.

To find the probability that the sum of both dice is a prime number, you need to divide the number of successful outcomes (15) by the total number of possible outcomes (36).

So, the probability of rolling a prime sum is 15/36, which can be simplified to 5/12.