Two dice are thrown at the same time.

Two dice are thrown at the same time. What is the probability that the sum of the numbers on the dice is greater than 7?

1. When two dice are rolled simultaneously, one may be interested in determining the likelihood that the total of the numbers displayed on the upper faces exceeds seven. This scenario is a common topic in probability theory, particularly relevant for students preparing for assessments such as the GCSE Maths Revision Course. Understanding how to calculate such probabilities involves analysing the possible outcomes that can arise from rolling two six-sided dice.

2. Each die has six faces, numbered from one to six, which results in a total of thirty-six possible combinations when two dice are rolled together. To find the probability that the sum of the numbers is greater than seven, one must first identify the specific combinations that yield sums exceeding this threshold. The sums that meet this criterion include eight, nine, ten, eleven, and twelve, and by systematically listing the combinations that produce these sums, one can ascertain the total number of favourable outcomes.

3. After identifying the successful outcomes, the next step is to calculate the probability by dividing the number of favourable outcomes by the total number of possible outcomes, which is thirty-six. This calculation provides a clear understanding of the likelihood of rolling a sum greater than seven. Such exercises not only enhance one’s grasp of probability but also serve as valuable practice for students engaged in the GCSE Maths Revision Course, reinforcing their analytical skills and mathematical reasoning.