If A and B are two events such that $P(A)=0.7$,$\mathrm{P}(\mathrm{B})=0.4$ and $\mathrm{P}(\mathrm{A}\cap \overset{¯}{\mathrm{B}})=0.5$, where $\overset{¯}{\mathrm{B}}$ denotes the complement of B, then $P(B∣(A\cup \overset{¯}{B}))$ is equal:- [JEE Main 2025, 8 Apr (Shift 1)]

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YESPYQ · Accepted Answer

Correct answer: a) $\frac{1}{4}$. $P(A)=0.7$ $P(B)=0.4$ $P(A\cap \overset{‾}{B})=0.5$ $\begin{matrix}P(A)−P(A\cap B)=0.5 \ P(A\cap B)=0.2\end{matrix}$ $P(\frac{B}{A\cup \overset{-}{B}})=\frac{P(B\cap (A\cup \overset{-}{B}))}{P(A\cup \overset{-}{B})}=\frac{0.2}{0.8}=\frac{1}{4}$ WHERE $\begin{matrix}P(A\cup \overset{‾}{B})=P(A)+P(\overset{‾}{B})−P(A\cap \overset{‾}{B}) \ =0.7+0.6−0.5 \ =0.8\end{matrix}$

If A and B are two events such that \(P(A)=0.7\),\(\mathrm{P}(\mathrm{B})=0.4\) and \(\mathrm{P}(\mathrm{A}\cap \overset…

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