Question If E and F are independent events, prove or disprove that E and F are necessarily independent events.

Given that events E and F are independent, it is proved that E’ and F are necessarily independent events. In the question, we are asked to prove that E’ and F are necessarily independent events, given that E and F are independent events. Using set theory, we must remember that: E’ ∩ F = F – (E ∩ F). The complement of any event A, shown as A’, is given as A’ = U – A, where U is the universal set. The probability is shown as: P(A’) = 1 – P(A). Also, for any two independent events A and B, we know that: P(A ∩ B) = P(A).P(B). Now, we try to calculate, P(E’ ∩ F) = P(F) – P(E ∩ F) = P(F) – P(E).P(F) {Since, E and F are independent events} = {1 – P(E)}.P(F) = P(E’).P(F), which proves that E’ and F are necessarily independent. Thus, given that events E and F are independent, it is proved that E’ and F are necessarily independent events. Learn more about independent events at https://brainly.com/question/1374659 #SPJ4 The given question is incorrect. The correct question is: “If E and F are independent events, prove or disprove that E’ and F are necessarily independent events.” Reply

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