Two events $A$ and $B$ are mutually independent and
$$\mathrm { P } \left( B ^ { C } \right) = \frac { 1 } { 3 } , \mathrm { P } ( A \mid B ) = \frac { 1 } { 2 }$$
What is the value of $\mathrm { P } ( A ) \mathrm { P } ( B )$? (Here, $B ^ { C }$ is the complement of $B$.) [3 points]\\
(1) $\frac { 5 } { 6 }$\\
(2) $\frac { 2 } { 3 }$\\
(3) $\frac { 1 } { 2 }$\\
(4) $\frac { 1 } { 3 }$\\
(5) $\frac { 1 } { 6 }$