1. The problem statement, all variables and given/known data A pair of dice is rolled once, what is the probability that neither a doublet nor the sum of 10 will appear 2. Relevant equations P(A) = 1 - P(A') Demorgans law (AUB)c = Ac ∩ B c 3. The attempt at a solution I know how to do the solution through brute force and listing out all the possible scenarios: (1,1), (1,2), (1,3) ...... (6,6) and doing it like that. But i wanted a more algebraic approach so I tried this: Let A = is a doublet Let B = sum of dices is 10 so then what I am looking for is P(Ac U Bc) and applying demorgans P(Ac U Bc) = P(A∩B )c using the law that Ac = 1 - A I got the final easy equation 1 - P(A ∩ B ) solving for this P(A) = 6/36 ...........(1,1),(2,2),(3,3),(4,4),(5,5),(6,6) P(B) = 3/36 ............(4,6), (5,5),(6,4) plug in numbers 1 - (6/36)*(3/36) != the answer of 7/9 Apparently, math lies, j.k. Can someone let me know what i am doing wrong?