For two independent events $A$ and $B$,
$$\mathrm { P } ( A \cap B ) = 2 \mathrm { P } \left( A \cap B ^ { c } \right) , \quad \mathrm { P } \left( A ^ { c } \cap B \right) = \frac { 1 } { 12 }$$
find the value of $\mathrm { P } ( A )$. (Given that $\mathrm { P } ( A ) \neq 0$.) [3 points]\\
(1) $\frac { 1 } { 2 }$\\
(2) $\frac { 5 } { 8 }$\\
(3) $\frac { 3 } { 4 }$\\
(4) $\frac { 7 } { 8 }$\\
(5) $\frac { 15 } { 16 }$