Question: prove that if a and b are independent events then their complements are also independent?
Answer: Independence: A and B are called independent if they satisfy the product formula P(A ∩ B) = P(A)P(B). P(A|B) = P(A ∩ B) P(B) , ... Independence of complements: If A and B are independent, then so are A and B , A and B, and A and B .