Question

Prove that if e and f are independent events, then so are the events e' and f'.

Answer 1

Hey !!

Since, E and F are independent events

=>  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 ∩ F') = P(E).P(F')

Hence, E' and F' are independent events.

Good luck !