#### Question

#### Solution

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

Is there an error in this question or solution?

Solution Prove that If E and F Are Independent Events, Then the Events E and F' Are Also Independent. Concept: Independent Events.