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If A and B are two events such that A≠∅A \neq \emptyset, B ≠∅\neq \emptyset, then which of following is/are TRUE:

A. P(B/A)=P(A).P(B)P(B/A)=P(A).P(B)

B. P(B/A)=P(A∩B)P(A)P(B/A)=\frac{P(A\cap B)}{P(A)}

C. P(A′/B′)=1−P(A∪B)1−P(B)P(A'/B')=\frac{1-P(A\cup B)}{1-P(B)}

D. P(B/A).P(A/B)=2P(B/A).P(A/B)=2

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 2

B is the definition of conditional probability, so it is true. For C, P(A′/B′)=P(A′∩B′)P(B′)=1−P(A∪B)1−P(B)P(A'/B')=\frac{P(A'\cap B')}{P(B')}=\frac{1-P(A\cup B)}{1-P(B)}, true. A holds only in the special independent case and is not an identity, and D is impossible since probabilities cannot exceed 1.

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