If A and B are independent, then ALL of these pairs are also independent:

• A and B'
• A' and B
• A' and B'

Proof sketch: P(A intersect B') = P(A) - P(A intersect B) = P(A) - P(A)P(B) = P(A)(1 - P(B)) = P(A)P(B').

For three events A, B, C to be mutually independent, ALL FOUR conditions must hold:

1. P(A intersect B) = P(A)P(B)
2. P(B intersect C) = P(B)P(C)
3. P(A intersect C) = P(A)P(C)
4. P(A intersect B intersect C) = P(A)P(B)P(C)

Pairwise independence (conditions 1-3) does NOT imply mutual independence. JEE has tested this distinction.