1. The problem statement, all variables and given/known data Given P(AUBUCUD), expand 3. The attempt at a solution I approached the solution by procedurally drawing Vann Diagrams, building from AUB to AUBUCUD (Not included); Please do check if my line of reasoning is sound. (let "n" be the intersection, AND) 1) P(AUB): P(A) + P(B) - P(AnB) [subtract the extra section, this is repeated at the end of subsequent steps] 2) P((AUB)UC): P(AUB) + P(C) - P((AUB)nC) 3) P((AUBUC)UD): P((AUB)UC) + P(D) - P((AUBUC)nD) Substituting backwards, hence A(AUBUCUD)= P(AUB) + P(C) - P((AUB)nC) + P(D) - P((AUBUC)nD) A(AUBUCUD)= P(A) + P(B) - P(AnB) + P(C) - P((AUB)nC) + P(D) - P((AUBUC)nD) (Solved) Also, do inform me if there is any more efficient way to put this. Thank you for your time.