Let A and B be two events. Then which of the following statements are TRUE?
(A) $P(B|A) =\frac{P(A∩B)}{P(A)}$, provided $P(A) ≠ 0$
(B) $P(B')=1+ P(B)$
(C) $P(A∪B) = P(A) + P(B) + P(A∩B)$
(D) $P(A∩B) = P(A).P(B)$ If A and B are independent events
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) and (D) only **
(A) $P(B|A)=\frac{P(A\cap B)}{P(A)}$, correct definition of conditional probability.
(B) $P(B')=1-P(B)$, hence false.
(C) $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, not $+$, so false.
(D) $P(A\cap B)=P(A)\cdot P(B)$ for independent events, true.
Correct statements: (A) and (D)