UGC NET Questions (Paper – 1)

This option is correct because the probability of an event and its complement must sum to 1. If P(A) = p, then P(A') = 1 − p. This follows directly from the rule that A and A' are mutually exclusive and exhaustive. Therefore, the complement has probability 1 − p.

Option A:
If we use p as the probability of A', then P(A) + P(A') would be p + p = 2p, which equals 1 only when p = 1/2. This does not hold in general and contradicts probability axioms. Hence, this option is incorrect.

Option B:
The expression 1/p would usually exceed 1 for p less than 1 and is not bounded between 0 and 1. Probabilities cannot exceed 1, so this form cannot represent the complement probability.

Option C:
The expression p² is smaller than p for values between 0 and 1 and does not generally satisfy P(A) + P(A') = 1. It is just another function of p, not the complement. Thus, this option is not correct.

Option D:
The value 1 − p ensures that P(A) + P(A') equals 1, satisfying the basic complement rule. It also remains between 0 and 1 whenever p is between 0 and 1. Therefore, this formula correctly represents P(A').