Which of the following statements are correct?
(A) If \(E\) and \(F\) are independent events then \(P(E \cap F)=P(E) P(F)\)
(B) If \(E\) and \(F\) are mutually exclusive events, then \(P(E \cup F)=P(E)+P(F)-P(E) P(F)\)
(C) The conditional probability of an event \(E\), given the occurrence of the event \(F\) is given by \(\frac{P(E \cap F)}{P\left(F^{\prime}\right)}, P(F) \neq 0\)
(D) If \(E\) and \(F\) be the events associated with the sample space \(S\) of an experiment, then \(P(\bar{E} \mid F)=2-P(E \mid F)\)
Choose the correct answer from the options given below:

1. A (A) and (C) only
2. B (A), (B) and (C) only
3. C (B) and (D) only
4. D (C) and (D) only