If $P (A) = 1/3$ , $P (B) = 1/2$ and $P (A \cap B) = 1/4$ , then what is the value of $P (A^{C} \cap B^{C})$ ?

Question

Question

This question was previously asked in

NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)

Answer 1

Calculation:

Given,

We need to calculate, the probability that neither A nor B occurs.

Using the complement rule:

Now, apply the inclusion-exclusion formula to find :

Substitute the given values:

To simplify:

Now, calculate :

Hence, the correct answer is Option 2.

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