P(A∩B)=0.1,P(A∣B) and P(B∣A) are the roots of the equation 12x2−7x+1=0 $\begin{aligned}
& \Rightarrow \quad P(A \mid B) P(B \mid A)=\frac{1}{12} \
& \Rightarrow \quad \frac{P(A \cap B)}{P(B)} \times \frac{P(A \cap B)}{P(A)}=\frac{1}{12} \
& \Rightarrow \quad P(A) P(B)=12(0.1)^2 \
& =0.12
\end{aligned}Also,P(A \mid B)+P(B \mid A)=\frac{7}{12}\begin{aligned}
\Rightarrow & P(A \cap B)\left(\frac{1}{P(B)}+\frac{1}{P(A)}\right)=\frac{7}{12} \
\Rightarrow & P(A)+P(B)=\frac{7}{12} \times \frac{0.12}{0.1} \
\Rightarrow & P(A)+P(B)=0.7 \
& \frac{P(\bar{A} \cup \bar{B})}{P(\bar{A} \cap \bar{B})}=\frac{P(\overline{A \cap B})}{P(\overline{A U B})} \
& =\frac{1-P(A \cap B)}{1-P(A \cup B)} \
& =\frac{1-0.1}{1-(0.7-0.1)}=\frac{0.9}{0.4}=\frac{9}{4}
\end{aligned}$