Question

If A and B are independent events such that 0 < P(A) < 1 and 0 < P(B) < 1., then which of the following is not correct?
(a) A and B are mutually exclusive
(b) A and $\overline{B}$ are independent
(c) $\overline{A}$ and B are independent
(d) $\overline{A}\mathrm{and}\overline{B}$ are independent

Answer 1

If A and B are independent events then P(A∩B) = P(A) P(B) ≠ 0
Since 0 < P(A) < 1 and 0 < P(B) < 1
∴ A and B can never be mutually exclusive and A and $\overline{B}$ are also independent
Similarly $\overline{A}\mathrm{and}\overline{B}$, Also $\overline{A}$ and B are independent

Hence, the correct answer is option A.