Q268 / 270 · NDA 2025 (Phase 2) · Mathematics
If $P(A) = 0.3$, $P(B) = 0.4$ and $P(A|B) = 0.5$, then what is the value of $P(B|A)$?
- A$0.325$
- B$0.333$
- C$0.375$
- Correct answerD$0.667$
Solution
Given $P(A) = 0.3$, $P(B) = 0.4$ and $P(A|B) = 0.5$.
Using the formula for conditional probability:
$P(A|B) = \dfrac{P(A \cap B)}{P(B)}$
$0.5 = \dfrac{P(A \cap B)}{0.4}$
$P(A \cap B) = 0.5 \times 0.4 = 0.2$
Now, finding $P(B|A)$:
$P(B|A) = \dfrac{P(A \cap B)}{P(A)}$
$P(B|A) = \dfrac{0.2}{0.3} = \dfrac{2}{3} \approx 0.667$
Answer: $0.667$
Using the formula for conditional probability:
$P(A|B) = \dfrac{P(A \cap B)}{P(B)}$
$0.5 = \dfrac{P(A \cap B)}{0.4}$
$P(A \cap B) = 0.5 \times 0.4 = 0.2$
Now, finding $P(B|A)$:
$P(B|A) = \dfrac{P(A \cap B)}{P(A)}$
$P(B|A) = \dfrac{0.2}{0.3} = \dfrac{2}{3} \approx 0.667$
Answer: $0.667$
Hence, the correct answer is option: 'D'.