Which of the following statements are correct?
(A) If E and F are independent events then $P(E∩F) = P(E) P(F)$
(B) If E and F are mutually exclusive events, then $P(E∪F) = P(E) + P(F) - P(E).P(F)$
(C) The conditional probability of an event E, given the occurrence of the event F is given by $\frac{P(E∩F)}{P(F)},P(F)≠0$
(D) If E and F be the events associated with the sample space S of an experiment, then $P (\bar E|F) = 2 − P(E|F)$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) and (C) only
(A) If $E$ and $F$ are independent events then $P(E\cap F)=P(E)P(F)$
This is the definition of independence.
True
(B) If $E$ and $F$ are mutually exclusive events, then $P(E\cup F)=P(E)+P(F)-P(E)P(F)$
For mutually exclusive events $P(E\cap F)=0$, so $P(E\cup F)=P(E)+P(F)$
Hence this statement is false.
False
(C) The conditional probability of $E$ given $F$ is $\frac{P(E\cap F)}{P(F)},\;P(F)\ne0$
This is the definition of conditional probability.
True
(D) $P(\bar E|F)=2-P(E|F)$
But $P(\bar E|F)=1-P(E|F)$
Hence false.
The correct statements are (A) and (C).