Question

Prove that if E and F are independent events, then the events E and F' are also independent. 

Answer 1

Two events E and F are independent if

P(E ∩ F) = P(E).P(F)

Now,

P(E ∩ F')=P(E and not F)

=P(E) - P(E ∩ F) = P(E)- P(E).P(F)                    [∵   E and F are independent events]

=P(E)[1 - P(F)] = P(E).P(F')

∴ P(E ∩ F') = P(E).P(F')

Hence, E and F' are independent events