Q269 / 270 · NDA 2025 (Phase 2) · Mathematics
If $P(A) = 1/3$, $P(B) = 1/2$ and $P(A \cap B) = 1/4$, then what is the value of $P(\bar{A} \cup B)$?
- A$7/12$
- B$2/3$
- C$3/4$
- Correct answerD$11/12$
Solution
Using De Morgan's laws, $P(\bar{A} \cup B) = 1 - P(A \cap \bar{B})$
$P(A \cap \bar{B}) = P(A) - P(A \cap B)$
Substituting the given values:
$P(A \cap \bar{B}) = \dfrac{1}{3} - \dfrac{1}{4} = \dfrac{1}{12}$
Therefore, $P(\bar{A} \cup B) = 1 - \dfrac{1}{12} = \dfrac{11}{12}$
Answer: $11/12$
$P(A \cap \bar{B}) = P(A) - P(A \cap B)$
Substituting the given values:
$P(A \cap \bar{B}) = \dfrac{1}{3} - \dfrac{1}{4} = \dfrac{1}{12}$
Therefore, $P(\bar{A} \cup B) = 1 - \dfrac{1}{12} = \dfrac{11}{12}$
Answer: $11/12$
Hence, the correct answer is option: 'D'.