Question
Prove that if E and F are independent events, then the events E and F' are also independent.
Solution
Two events E and F are independent if
P(E ∩ F) = P(E).P(F)
Now,
P(E ∩ F') = P(E) – P(E ∩ F)
= P(E) – P(E). P(F)
= P(E)[1 – P(F)]
= P(E).P(F')
E and F' are independent events.
P(E ∩ F) = P(E).P(F)
Hence prove
