Final answer:
To find the probability that X is 2, 11, or 12 when rolling a pair of fair dice, we need to find the number of favorable outcomes and divide it by the total number of possible outcomes. There is only one way to get a sum of 2 or 12, and there are 2 ways to get a sum of 11. So, the probability is 1/12.
Step-by-step explanation:
To find the probability that X is 2, 11, or 12 when rolling a pair of fair dice, we need to find the number of favorable outcomes and divide it by the total number of possible outcomes.
There is only one way to get a sum of 2 (rolling two ones), and there is only one way to get a sum of 12 (rolling two sixes). To get a sum of 11, we can either roll a 5 and a 6 or a 6 and a 5. So, there are 2 ways to get a sum of 11.
Since there are 36 possible outcomes when rolling two dice (6 possible outcomes for the first die multiplied by 6 possible outcomes for the second die), the probability of getting a sum of 2, 11, or 12 is (1 + 2) / 36 = 3 / 36 = 1 / 12.