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\left(B \mid (A \cup \overline{B})\right) is equal to

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Answer: C. \frac{1}{4} \begin{aligned} & \mathrm{P}(\mathrm{~A})=\frac{7}{10}, \mathrm{P}(\mathrm{~B})=\frac{4}{10} \ & \mathrm{P}(\mathrm{~A} \cup \overline{\mathrm{~B}})=\frac{5}{10} \ & \mathrm{P}\left(\frac{\mathrm{~B}}{\mathrm{~A} \cup \overline{\mathrm{~B}}}ight)=\frac{\mathrm{P}(\mathrm{~B} \cap(\mathrm{~A} \cup \overline{\mathrm{~B}}))}{\mathrm{P}(\mathrm{~A} \cup \overline{\mathrm{~B}})} \ & =\frac{\mathrm{P}((\mathrm{~B} \cap \overline{\mathrm{~B}}) \cup(\mathrm{B} \cap \mathrm{~A}))}{\mathrm{P}(\mathrm{~A} \cup \overline{\mathrm{~B}})}=\frac{\mathrm{P}(\mathrm{~A} \cap \mathrm{~B})}{\mathrm{P}(\mathrm{~A} \cup \overline{\mathrm{~B}})} \end{aligned} \begin{aligned} & =\frac{\mathrm{P}(\mathrm{~A})-\mathrm{P}(\mathrm{~A} \cap \overline{\mathrm{~B}})}{\mathrm{P}(\mathrm{~A})+\mathrm{P}(\overline{\mathrm{~B}})-\mathrm{P}(\mathrm{~A} \cap \overline{\mathrm{~B}})}=\frac{\frac{7}{10}-\frac{5}{10}}{\frac{7}{10}+\left(1-\frac{4}{10}ight)-\frac{5}{10}} \ & =\frac{2}{8}=\frac{1}{4} \end{aligned}

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 $P\left(B \mid (A \cup \overline{B})\right)$ is equal to

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