12. Two fair dice are rolled. Find the probability that both dice have a sum of 10.

To find the probability that the sum of two rolled fair dice is 10, first, identify the possible combinations that yield this sum. The pairs (4, 6), (5, 5), and (6, 4) are the only combinations, making a total of 3 favorable outcomes. Since there are 36 possible outcomes when rolling two dice (6 sides on the first die times 6 on the second), the probability is thus 3/36, which simplifies to 1/12. The beauty of probability problems like this is you can visualize it in a fun way—think of each die as a unique character in a game trying to team up to reach a score of 10. Each combination is a different strategy they can use, and while they have some options, not every combination leads to victory!