UGC NET Questions (Paper – 1)

Statements A and B are fundamental facts about complements, D describes the multiplication rule for independent events and E is true because working with complements, like “at least one” via “1 − P(none)”, often simplifies calculations. Statement C is false because for mutually exclusive events, P(A and B) = 0, not P(A) + P(B), which is instead P(A or B) for such events. Therefore, the combination A, B, D and E only is correct.

Option A:
Option A is incomplete since it omits E and thus does not state explicitly the strategic advantage of using complementary events to simplify some NET probability questions.

Option B:
Option B is also incomplete because it leaves out D, thereby ignoring the key rule for independent events, which is central to many probability computations. Without D, the treatment of joint events is missing.

Option C:
Option C is wrong because it excludes A and consequently fails to express the basic identity P(A) + P(not A) = 1, and it still does not remove C, the incorrect equality about mutually exclusive events.

Option D:
Option D is correct as it collects all true statements and rejects C, which confuses “and” with “or” probabilities for mutually exclusive events. It represents how complementary and independent events are used in exam-level problems.

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.