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Prove that If E and F Are Independent Events, Then the Events E and F' Are Also Independent. - CBSE (Science) Class 12 - Mathematics

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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 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

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