Independence Extended. Three events A, B, and C are said to be independent if P(A & B) = P(A) · P(B), P(A & C) = P(A) · P(C), P(B & C) = P(B) · P(C), and P(A & B & C) = P(A) · P(B) · P(C).

What is required for four events to be independent? Explain your definition in words.