Q90 / 180 · COMEDK 2025 (10 May Shift 2) · Mathematics
If for two events $A$ and $B, P(A-B)=\dfrac{1}{5}$ and $P(A)=\dfrac{3}{5}$ then $P(B / A)=$
- A$\dfrac{3}{5}$
- Correct answerB$\dfrac{2}{3}$
- C$\dfrac{2}{5}$
- D$\dfrac{1}{2}$
Solution
The probability of the event $A-B$ is given by $P(A-B) = P(A) - P(A \cap B)$.
Given $P(A-B) = \dfrac{1}{5}$ and $P(A) = \dfrac{3}{5}$, we substitute these values into the equation:
$\dfrac{1}{5} = \dfrac{3}{5} - P(A \cap B)$
$P(A \cap B) = \dfrac{3}{5} - \dfrac{1}{5} = \dfrac{2}{5}$
The conditional probability $P(B/A)$ is defined as $P(B/A) = \dfrac{P(A \cap B)}{P(A)}$.
Substituting the known values:
$P(B/A) = \dfrac{2/5}{3/5} = \dfrac{2}{3}$
Answer: $\dfrac{2}{3}$
Given $P(A-B) = \dfrac{1}{5}$ and $P(A) = \dfrac{3}{5}$, we substitute these values into the equation:
$\dfrac{1}{5} = \dfrac{3}{5} - P(A \cap B)$
$P(A \cap B) = \dfrac{3}{5} - \dfrac{1}{5} = \dfrac{2}{5}$
The conditional probability $P(B/A)$ is defined as $P(B/A) = \dfrac{P(A \cap B)}{P(A)}$.
Substituting the known values:
$P(B/A) = \dfrac{2/5}{3/5} = \dfrac{2}{3}$
Answer: $\dfrac{2}{3}$
Hence, the correct answer is option: 'B'.