If A and B are two events such that \(P(A \cap B)=0.1\), and \(P(A \mid B)\) and \(P(B \mid A)\) are the roots of the eq…

If A and B are two events such that \(P(A \cap B)=0.1\), and \(P(A \mid B)\) and \(P(B \mid A)\) are the roots of the equation \(12 x^2-7 x+1=0\), then the value of \(\frac{\mathrm{P}(\overline{\mathrm{A}} \cup \overline{\mathrm{B}})}{\mathrm{P}(\overline{\mathrm{A}} \cap \overline{\mathrm{B}})}\) is:

[JEE Main 2025, 22 Jan (Shift 2)]