Traditional definition of independence says that events A and Bare
independent if and only if P(A n B)=P(A)×P(B). Show that P(A nB)=P(A)×P(B) if
and only if
a. P(A n B’) = P(A) × P(B’)b. P(A’ n B’) = P(A’) × P(B’)
You may use these without proof in your solutions:
o P(A n B’) = P(A) – P(A n B). [This can be proven by first showingthat
(A ∩ B ′ ) ∪̇ (A ∩ B) = A and using the Addition Rule.]
o P(A n B) = 1 – P(A’ n B’). [This can be proven by noting thatunder de
Morgan’s Law, (A n B)’ = A’ n B’.]
