If A and B are two events such that $\mathrm{P}(\mathrm{A})=0.7$, $\mathrm{P}(\mathrm{B})=0.4$ and $\mathrm{P}(\mathrm{A} \cap \overline{\mathrm{B}})=0.5$, where $\overline{\mathrm{B}}$ denotes the complement of B, then $\mathrm{P}(\mathrm{B} \mid(\mathrm{A} \cup \overline{\mathrm{B}}))$ is equal to

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Probability

If A and B are two events such that

P (A) = 0.7

P (B) = 0.4

and

P (A \cap \overline{B}) = 0.5

, where

\overline{B}

denotes the complement of B, then

P (B ∣ (A \cup \overline{B}))

is equal to

Answer: (A)

From

P (A \cap \overline{B}) = 0.5

P (A \cap B) = P (A) - P (A \cap \overline{B}) = 0.7 - 0.5 = 0.2

. Because

B \cap (A \cup \overline{B}) = (B \cap A) \cup (B \cap \overline{B}) = A \cap B

, the numerator is

0.2

. Also

P (A \cup \overline{B}) = P (A) + P (\overline{B}) - P (A \cap \overline{B}) = 0.7 + 0.6 - 0.5 = 0.8

. Hence

P (B ∣ (A \cup \overline{B})) = \frac{0.2}{0.8} = \frac{1}{4}

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Single correct option