Independence and mutual exclusivity – UGC NET Question

B is the definition of independence: P(A ∩ B) = P(A)P(B). C is correct because mutually exclusive events with positive probabilities have P(A ∩ B)=0 but P(A)P(B)>0, so they cannot be independent. D is true because independence carries over to complements. A is false (addition relates to mutually exclusive unions, not independence). E is false because for independent events P(A|B) = P(A), not 0. Therefore B, C and D only are correct.

Option A:
Option A is incomplete because it includes only B and leaves out C and D, which are also correct statements.

Option B:
Option B is correct as it includes exactly the true statements and excludes A and E, which confuse addition/conditional probability with independence.

Option C:
Option C is wrong because it includes E, which misstates conditional probability under independence.

Option D:
Option D is incorrect because it includes A, which is not the criterion for independence.