If \(\mathrm{P}(\mathrm{A})=\frac{3}{10}, \mathrm{P}(\mathrm{B})=\frac{3}{5}, \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{3}{5}\), then \(\mathrm{P}(\mathrm{A} / \mathrm{B}) \times \mathrm{P}(\mathrm{B} / \mathrm{A})=\)

\(
\mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{B}}\right) \times \mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{A}}\right)=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{B})} \times \frac{\mathrm{P}(\mathrm{B} \cap \mathrm{A})}{\mathrm{P}(\mathrm{A})}
\)
We know that \(\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})\)
\(\frac{3}{5}=\frac{3}{10}+\frac{2}{5}-\mathrm{P}(\mathrm{A} \cap \mathrm{B}) \Rightarrow \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{10} \)
\( \therefore \text {Given expression}=\frac{\left(\frac{1}{10}\right)}{\left(\frac{2}{5}\right)} \times \frac{\left(\frac{1}{10}\right)}{\left(\frac{3}{10}\right)}=\frac{1}{4}~ \times\) \(\frac{1}{3}=\frac{1}{12}\)