If events and are independent

MATHEMATICS · Single correct · A Level · Mathematics · Probability · Probability

Problem

If events AA and BB are independent, which statement about their complements is always true? (a) Only the pair (A‾,B‾)(\overline{A},\overline{B}) is independent. (b) None of the complement pairs are necessarily independent. (c) All three pairs (A‾,B)(\overline{A},B), (A,B‾)(A,\overline{B}), and (A‾,B‾)(\overline{A},\overline{B}) are independent. (d) The pairs (A‾,B)(\overline{A},B) and (A,B‾)(A,\overline{B}) are independent but (A‾,B‾)(\overline{A},\overline{B}) may not be.

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