Question: if events a b and c are independent show that a and b union c are independent?
Answer: According to the definition of independent events, A and B∪C are independent if and only if P(A∩(B∪C))=P(A)P(B∪C). Since A and B and A and C are independent, I know that P(A∩B)=P(A)P(B)andP(A∩C)=P(A)P(C).