Two six-sided number cubes are rolled. What is the probability that the sum is greater than 3?

1. Each cube has 6 faces, so by the Multiplication Principle there are 6 times 6 = 36 equally likely outcomes. 2. Listing every sum above 3 would be long, so work with the complement instead. 3. The complement is a sum of 3 or less, which happens only on 1-1, 1-2 and 2-1. 4. So the complement has probability 3/36 = 1/12. 5. Apply the Complement Rule: the answer is 1 - 1/12. 6. That gives 11/12. 7. Reporting 1/12 answers the complement rather than the question, which is the standard slip with this method. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.7 Probability_