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1. 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.”

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