What is the probability of the sum of two fair dice being less than 12?

In this question, the interviewer is assessing your grasp of fundamental concepts in statistics, specifically probability theory. To respond, you should possess a basic comprehension of probability, particularly regarding the rolling of two dice. To determine the probability that the sum of the two dice is less than 12, you must recognize that the only scenario where the sum equals 12 occurs when both dice show a 6 (which represents one outcome out of a total of 36 possible outcomes). Additionally, you should be able to compute the overall number of potential outcomes when rolling two dice, which is 36 (6 outcomes for the first die multiplied by 6 for the second die). With this knowledge, you can then calculate the probability of the sum being less than 12.

The inquiry seeks the likelihood of the sum being under 12 when rolling two standard six-sided dice. The only scenario in which the sum will equal or exceed 12 occurs when both dice show a 6, resulting in a total of 12. This situation represents just one outcome among the 36 possible combinations when rolling two six-sided dice. Consequently, the probability that the sum will remain below 12 is 35 out of 36, which is roughly 97.22%.

When two dice are rolled, there are a total of 36 possible outcomes (6 options for the first die multiplied by 6 options for the second die). The only way to obtain a sum of 12 is if both dice show a 6, which can happen in just one specific way. Therefore, there is only one combination of rolls that results in a sum of 12, while all other combinations yield a sum less than 12. As a result, the probability of the sum being less than 12 is 35 out of 36, or roughly 97.22%.