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Question
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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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