Q115 / 180 · COMEDK 2026 (9 May Shift 2) · Mathematics
If $P(A \cup B) = 0.85$, $P(B) = 0.50$ and $P(A \cap B) = 0.30$. Then $P(A \cap B') =$
- A$0.55$
- Correct answerB$0.35$
- C$0.65$
- D$0.2$
Solution
Using the formula for the union of two events:
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$0.85 = P(A) + 0.50 - 0.30$
$P(A) = 0.65$
The probability of occurrence of only $A$ is given by:
$P(A \cap B') = P(A) - P(A \cap B)$
$P(A \cap B') = 0.65 - 0.30 = 0.35$
Answer: $0.35$
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$0.85 = P(A) + 0.50 - 0.30$
$P(A) = 0.65$
The probability of occurrence of only $A$ is given by:
$P(A \cap B') = P(A) - P(A \cap B)$
$P(A \cap B') = 0.65 - 0.30 = 0.35$
Answer: $0.35$
Hence, the correct answer is option: 'B'.