UGC NET Questions (Paper – 1)

Statements A, B, C and D together summarise the standard relationships between mutually exclusive and independent events. A correctly defines mutual exclusivity as events that cannot happen simultaneously. B properly describes independence in terms of unchanged probabilities. C follows because if two non-trivial events are mutually exclusive, their joint probability is zero and cannot equal the product of positive probabilities, so they are not independent. D restates the formal definition of independence using the product rule. E is false since mutual exclusivity and independence are distinct concepts, so the correct set is A, B, C and D only.

Option A:
Option A is incomplete because it omits D and thus fails to express the formal product definition of independence, even though A, B and C are true. The absence of D makes the description of independence less precise.

Option B:
Option B is correct as it combines the basic definitions and implications about mutual exclusivity and independence and excludes E, which wrongly equates the two. It matches the conceptual treatment of events found in NET-level probability questions.

Option C:
Option C is incorrect because it includes E, the false claim that mutual exclusivity and independence mean the same thing, and leaves out B, which is a core statement about independence. This mixture of error and omission invalidates the option.

Option D:
Option D is wrong as it drops A and includes only B, C and D, leaving out the explicit definition of mutual exclusivity while still not rejecting E. It therefore does not provide the complete and correct set of statements.

Statements C and E are the wrong statements here. A is correct because probabilities range from 0 to 1. B is true since probabilities of all mutually exclusive and exhaustive outcomes sum to 1. D correctly states that a certain event has probability 1. C is false because 0.7 indicates a more likely event than 0.4. E is false because P(A ∪ B) equals P(A) + P(B) only when A and B are mutually exclusive; otherwise the intersection must be subtracted. Therefore, the wrong statements are C and E only.

Option A:
Option A is incomplete because it selects only C as wrong and ignores E, which misapplies the addition rule for probabilities of unions.

Option B:
Option B is correct as it identifies both C and E as incorrect, thereby recognising that both comparative likelihood and union probabilities are mishandled in those statements.

Option C:
Option C is wrong since it mislabels A as wrong, even though A accurately describes the probability range, and still keeps C and E, mixing correct and incorrect judgments.

Option D:
Option D is incorrect because it classifies B and D as wrong despite them stating fundamental probability principles, and it omits E, which actually contains an error about unions.

This option is correct because one of the fundamental axioms of probability states that the total probability of all outcomes in a sample space is 1. When outcomes are mutually exclusive and exhaustive, exactly one of them must occur. Therefore, adding their probabilities must give 1. This ensures that some outcome always happens.

Option A:
A total probability of 0 would mean that no outcome can occur, which contradicts the idea of running an experiment. Probabilities must be non-negative and at least one outcome must have positive probability. Thus, the sum cannot be 0 for an actual experiment.

Option B:
The value 1 represents certainty that some outcome from the sample space will occur. Since mutually exclusive and exhaustive outcomes cover all possibilities without overlap, their probabilities must add up to 1. This matches the basic probability axiom, making this option correct.

Option C:
A sum of 1/2 would imply that there is only a 50% chance that any outcome in the declared space occurs. That would mean half the probability lies outside the listed outcomes, so the set would not be exhaustive. Hence, this value cannot be correct here.

Option D:
The value 100 without the percent sign does not fit the standard probability scale from 0 to 1. Even if interpreted as a percentage, it would correspond to 1 on the probability scale, but the question expects the probability value, not the percentage number. Therefore, 100 is not the right answer.

D is wrong because the total probability of all simple events in a well-defined sample space must sum to exactly 1, not more than 1. Statements A, B, C and E are correct: probabilities are bounded between 0 and 1, probabilities 0 and 1 represent impossibility and certainty within the model, mutually exclusive events have additive probabilities, and NET questions often test both conceptual understanding and simple calculations. Since only D contradicts the axioms of probability, the correct answer is the option that lists D only as wrong.

Option A:
Option A is correct because it isolates D as the single statement that violates the basic rule that the total probability over a sample space equals 1. It implicitly accepts that the other statements are consistent with elementary probability theory and exam practice.

Option B:
Option B is incorrect as it also treats A as wrong, even though A correctly states the allowed numerical range of probability values. By labelling A incorrect, this option misrepresents one of the most fundamental facts about probability.

Option C:
Option C is wrong because it groups C with D as wrong, despite C correctly stating the addition rule for mutually exclusive events. Including a true rule alongside a false statement makes this option invalid.

Option D:
Option D is also incorrect since it adds B and C to the set of wrong statements, even though both B and C are standard properties of probability. This option rejects several correct ideas along with the one incorrect statement.